Answer:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
Step-by-step explanation:
The information given for this case is:
[tex]\hat p_1 = 0.68 , \hat p_2 = 0.56[/tex]
[tex] n_1 = 70, n_2 =100[/tex]
We want to construct a confidence interval for the difference of proportions [tex]p_1 -p_2[/tex] and for this case this confidence interval is given by:
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
The confidence level is 0.95 so then the significance level would be [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] if we find the critical values for this confidence level we got:
[tex]z_{\alpha/2}= \pm 1.96[/tex]
And replacing the info we got:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
The 95% confidence interval is (0.257,-0.017).
To understand the calculations, check below.
Critical value:The critical value is a cut-off value that is used to mark the start of a region where the test statistic, obtained in hypothesis testing, is unlikely to fall in.
Given that,
[tex]n_1=70\\n_2=100\\\hat{p_1}=0.68\\\hat{p_1}=0.56\\SE=0.07\\\alpha=0.05[/tex]
The critical value is,
[tex]Z_{\frac{\alpha}{2} }=Z_{\frac{0.05}{2} }=1.96[/tex] (From standard normal probability table)
Therefore, the 95% confidence interval for the difference between population proportions [tex]p_1-p_2[/tex] is ,
[tex](\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times \sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2} ) }\\=(\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times SE\\=(0.68-0.56)\pm 1.96\times 0.07\\=0.12\pm 0.137\\=(0.257,-0.017)[/tex]
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In studying a random sample of 20 automotive batteries, the confidence interval (0.22,0.33) was constructed for the population standard deviation of the batteries' reserve capacity in hours. This population standard deviation should be less than 0.26 hour. Does the confidence interval suggest that the variation in the batteries' reserve capacities is at an acceptable level? Explain your reasoning.
Answer:
NO.
Step-by-step explanation:
From the question, we are given a random sample of 20 automotive batteries, a confidence interval =(0.22,0.33). Also, the population standard deviation is said to be less than 0.26 hour.
The confidence interval does NOT suggest that the variation in the batteries' reserve capacities is at an acceptable level.
REASON: If you look at the confidence interval, we can see that it contains the value for the standard deviation that is 0.26 and even MORE value than 0.26.
This does not give us any suggestion that the standard deviation is less than 0.26.
Final answer:
The confidence interval suggests that the variation in the batteries' reserve capacities is not at an acceptable level because the interval (0.22, 0.33) lies above the acceptable standard deviation of less than 0.26 hour.
Explanation:
In the context of the question, a constructed confidence interval for the population standard deviation of automotive batteries' reserve capacity is (0.22, 0.33 hours). To evaluate whether the variation in the batteries' reserve capacities is at an acceptable level, we would compare the interval to the stated acceptable level of a population standard deviation which should be less than 0.26 hour. Since the lower bound of the interval is above 0.22 and the entire confidence interval lies above 0.26, this suggests that the variability may be higher than the acceptable level, hence the variation is not at an acceptable level according to the specified criteria.
As for the example related to the NeverReady batteries, it demonstrates the use of sample data to question a company's claim about product performance by calculating the probability of obtaining a sample with a mean as low as or lower than observed when assuming that the company's claim is true. If the probability is very low, it casts doubt on the claim.
Timothy creates a game in which the player rolls 4 dice. What is the probability in this game of having exactly two dice or more land on a five?
A. 0.016
B. 0.132
C. 0.868
D. 0.984
Answer:
B. 0.132
Step-by-step explanation:
For each time the dice is thrown, there are only two possible outcomes. Either it lands on a five, or it does not. The probability of a throw landing on a five is independent of other throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Timothy creates a game in which the player rolls 4 dice.
This means that [tex]n = 4[/tex]
The dice can land in 6 numbers, one of which is 5.
This means that [tex]p = \frac{1}{6}[/tex]
What is the probability in this game of having exactly two dice or more land on a five?
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{2} = 0.116[/tex]
[tex]P(X = 3) = C_{4,2}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015[/tex]
[tex]P(X = 4) = C_{4,4}.(\frac{1}{6})^{4}.(\frac{5}{6})^{0} = 0.001[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.116 + 0.015 + 0.001 = 0.132[/tex]
So the correct answer is:
B. 0.132
The probability of having exactly two dice or more land on a five is: 0.132.
To determine the probability of having exactly two dice or more land on a five when rolling four dice, we first need to calculate the probabilities of each possible outcome involving getting at least two fives.
1: Define the basic probabilities
Each die has 6 faces, so the probability ( p ) of rolling a five on a single die is:
[tex]\[ p = \frac{1}{6} \]The probability \( q \) of not rolling a five on a single die is:\[ q = 1 - p = \frac{5}{6} \][/tex]
2: Define the number of dice rolls
We are rolling 4 dice.
3: Calculate probabilities for 0, 1, 2, 3, and 4 fives
We use the binomial distribution formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]where \( n = 4 \), \( p = \frac{1}{6} \), and \( k \)[/tex] is the number of fives rolled.
Probability of rolling exactly 0 fives (\( k = 0 \)):
[tex]\[ P(X = 0) = \binom{4}{0} \left(\frac{1}{6}\right)^0 \left(\frac{5}{6}\right)^4 = 1 \times 1 \times \left(\frac{5}{6}\right)^4 = \left(\frac{5}{6}\right)^4 \][/tex]
Probability of rolling exactly 1 five (\( k = 1 \)):
[tex]\[ P(X = 1) = \binom{4}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 \]Probability of rolling exactly 2 fives (\( k = 2 \)):\[ P(X = 2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2 = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 \][/tex]
[tex]Probability of rolling exactly 3 fives (\( k = 3 \)):\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \])^1 \]Probability of rolling exactly 4 fives (\( k = 4 \)):[/tex]
[tex]\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \][/tex]
4: Sum probabilities for \( k \geq 2 \)
We need to find \( P(X \geq 2) \), which is:
[tex]\[ P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \][/tex]
5: Perform calculations
[tex]\[P(X = 0) = \left(\frac{5}{6}\right)^4 \approx 0.4823\]\[P(X = 1) = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{125}{216}\right) \approx 0.3858\]\[P(X = 2) = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} \approx 0.1157\][/tex]
[tex]\[P(X = 3) = 4 \times \left(\frac{1}{6}\right)^3 \times \frac{5}{6} = 4 \times \frac{1}{216} \times \frac{5}{6} = \frac{20}{1296} \approx 0.0154\]\[P(X = 4) = \left(\frac{1}{6}\right)^4 = \frac{1}{1296} \approx 0.0008\][/tex]
6: Summing up [tex]\( P(X \geq 2) \)[/tex]
[tex]\[P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \approx 0.1157 + 0.0154 + 0.0008 = 0.1319\][/tex]
Rounding this to three decimal places, we get 0.132.
Thus, the probability of having exactly two dice or more land on a five is:
[tex]\[ \boxed{0.132} \][/tex].
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. Using the empirical rule, what percentage of the boys are between 65 and 75 inches tall?
Answer:
68%
Step-by-step explanation:
Final answer:
Using the empirical rule for normal distribution, approximately 68% of the boys at the all boys school with a mean height of 70 inches and a standard deviation of 5 inches are between 65 and 75 inches tall.
Explanation:
According to the empirical rule (also known as the 68-95-99.7 rule), for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
And around 99.7% falls within three standard deviations of the mean.
In the case of the all boys school with a mean height of 70 inches and standard deviation of 5 inches, the range between 65 inches (70 - 5) and 75 inches (70 + 5) represents one standard deviation from the mean on either side. Thus, using the empirical rule, approximately 68% of the boys are between 65 and 75 inches tall.
For what value of a does 9=(1/27)^2+3
Answer:
if a= (1/27)^2 + 3, then a is about 3.00137
Step-by-step explanation:
I assume you have a typo here.
Your equation should be a = (1/27)^2 + 3 ...
If that is so, a = (1/27)^2 + 3 = 3.00137...
The domain of f(x) = 4x is The range of f(x) = 4x is
Answer:
all real numbers
y>0
Step-by-step explanation:
The range of f(x) = 4x is all real numbers.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Therefore, The range of f(x) = 4x is all real numbers.
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The graph for the equation y = x minus 4 is shown below.
On a coordinate plane, a line goes through (0, negative 4) and (4, 0).
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
y minus x = negative 4
y minus x = negative 2
y minus 4 = x
y + 4 x = 1
Answer:
The answer is y minus x = negative 4
Step-by-step explanation:
PLEASE HELP ME
I DONT UNDERSTAND
Answer: its letter A
Step-by-step explanation:
Answer:
145
Step-by-step explanation:
This is pretty simple, the three angles inside the triangle equal to 180 degrees, so if you add 80 and 65 and subtract that from 180, you get 35. So two angles that are connected to a single line equal to 180, so you just subtract 35 from 180 to get 145. Therefore, <1 = 145.
An English teacher needs to pick 9 books to put on his reading list for the next school year, and he needs to plan the order in which they should be read. He has narrowed down his choices to 19 novels, 22 plays, and 22 nonfiction books. If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
Answer:
The total number of reading schedules is [tex]83.3927415552\cdot 10^{13}[/tex]
Step-by-step explanation:
Recall that if we have n elements, the number of ways in which we can choose k elements without minding the order is [tex]\binom{n}{k}=\frac{n!}{(n-k)! k!}[/tex].
At first, suppose that we have already chosen 9 books. If we want to number the order in which we are reading this books from 1 to 9, for position 1 we have 9 options, for position 2, we have 8 and so on. Using the multiplication principle, we have that the number of ways or arranging 9 books is 9!
Recall that we want the same amount from novels, plays and nonfiction. That is, we are choosing 3 books from each group. We can easy calculate the total number of ways of choosing the 9 books by simply multiplying the number of ways we choose 3 from each cathegory. Hence the total number of ways of choosing the 9 books is
[tex]\binom{9}{3}\cdot \binom{22}{3}\cdot \binom{22}{3}[/tex]
For each selection of 9 books, we have 9! different ways of organizing them, then the total number is
[tex]\binom{9}{3}\cdot \binom{22}{3}\cdot \binom{22}{3}\cdot 9! = 83.3927415552\cdot 10^{13}[/tex]
The sum of 3 consecutive integers is 60. What is the value of the third integer?
Answer:
x=19
Step-by-step explanation:
The consecutive integers will be x, x+1 and x+2 since consecutive integers have a pattern.
So, the equation is x+x+1+x+2=60
Solve:
x+x+1+x+2=60
3x+3=60
Subtract 3 on both sides:
3x+3-3=60-3
3x=57
Divide by 3
3x/3=57/3
x=19
The perimeter of a triangle DEF is 81 units. The length of side DE is twice the length of side EF, and the length of side DF is 4 units less than the length of side DE. Let s represent the length, in units, of side EF. Write an equation that can be used to find s
Answer:
5s = 85
Step-by-step explanation:
Perimeter of our triangle = DE + EF + DF = 81 units
We know from the question that
The length of side DE is twice the length of side EF
DE = 2EF
and the length of side DF is 4 units less than the length of side DE
DF = DE - 4
We can replace EF with s in our equations
DE = 2s
And now we can replace DE from the other equation
DF = DE - 4
DF = 2s - 4
If the perimeter of our triangle = DE + EF + DF = 81 units
We will replace the sides with our new values
Perimeter = 2s + s + 2s - 4 = 81
We can put this as our answer, or we can simplify further
Simplify by adding 4 to both sides
2s + s + 2s - 4 + 4 = 81 + 4
Simplify
2s + s + 2s = 85
Simplify
5s = 85
Since the question only asked for an equation, not for us to solve it, we can stop here
(If you wanted to solve for s, just divide both sides by 5)
5s / 5 = 85 / 5
s = 17
Answer:
81 = s + 2s + (2s -4)
Step-by-step explanation:
You are given a bag with 8 green marbles, 6 blue marbles, 14 yellow marbles, and 12 red marbles. Find the theoretical probability of each random event. (Enter your probabilities as fractions.)
(a) Drawing a green marble
(b) Drawing a red marble
(c) Drawing a marble that is not yellow
The theoretical probability of drawing a green marble is 1/5, a red marble is 3/10, and a marble that is not yellow is 13/20 from a bag of 40 marbles with varying colors.
The question involves calculating the theoretical probability of drawing certain colored marbles from a bag with a mixed collection of marbles. To find the probability of each event, we can use the formula P(event) = Number of favorable outcomes / Total number of outcomes.
Drawing a green marble: There are 8 green marbles out of a total of 40 marbles. So, P(green) = 8/40 = 1/5.
Drawing a red marble: There are 12 red marbles out of a total of 40 marbles. So, P(red) = 12/40 = 3/10.
Drawing a marble that is not yellow: There are 26 marbles that are not yellow (8 green, 6 blue, and 12 red) out of a total of 40 marbles. So, P(not yellow) = 26/40 = 13/20.
A 40% antifreeze solution is to be mixed with a 70% antifreeze solution to get 240 liters of a 64% solution. How many liters of the 40% and how many liters of the 70% solutions will be used?
Answer:
We have 40% antifreeze and 70% antifreeze and we need to make 240 liters of 64% antifreeze.
We set up 2 equations where "f" is the 40 % and "s" is the 70%
A) f + s = 240
B) .40f + .70s = (.64 * 240) (or 153.6)
To solve both equations we multiply A) by -.40
A) -.40 f - .40 s = -96.00 then we add this to B)
B) .40f + .70s = 153.60
.30s = 57.6
s = 192
f = 48
48 liters of 40% = 19.20 liters of antifreeze
192 liters of 70% = 134.40 liters of antifreeze
That equals 153.60 liters of antifreeze in a TOTAL liquid amount of 240 liters.
Double Check
153.60 / 240 = 64% antifreeze.
Step-by-step explanation:
The distance between two cities on a map is 13 cm. What is the actual distance between the cities if the map is drawn at a scale of 1:50,000?
Answer:
65,000
Step-by-step explanation:
because the scale is 1:50,000, so just simply multiply by 50,000.
Answer:i am not going to answer htis question 4 u but i will tell u how 2 do it first u mulitply 50,000 by 13 then you convert the number of centimeters u get into kilometers (this is where most people get wrong cuz there 2 lazy to read the question.
It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and found no evidence to reject the null hypothesis at the 5% significance level. What is true regarding the p-value from this hypothesis test?
Answer:
Given:
Sample size, n = 20
Significance level = 5% = 0.05
Mean, u = 8
Here, the sample mean was not given.
Here the null and alternative hypothesis will be:
H0 : u = 8
H1 : u < 8
In this case, since there is no evidence to reject the null hypothesis, H0, at 0.05 level of significance, we can say that the p-value is greater than the level of significance, 0.05.
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 2 and less than 5. The probability of being dealt a card greater than 2 and less than 5 is........
Final answer:
The probability of being dealt a card greater than 2 and less than 5 from a standard deck of 52 cards is 2/13.
Explanation:
The probability of being dealt a card greater than 2 and less than 5 from a standard 52-card deck means you are looking for 3s and 4s from each suit (hearts, spades, clubs, diamonds).
For each suit, there is one 3 and one 4, making a total of 8 possible cards (2 cards per suit multiplied by 4 suits). To calculate the probability, you divide the number of favorable outcomes by the number of possible outcomes. So, this probability is 8/52, which simplifies to 2/13 when reduced.
A chef got 17 bags of onions. The red onions came in bags of 4 and the yellow onions came in bags of 6. If the chef got a total of 88 onions, how many bags of each type of onion did he get?
Answer:
7 bags red onions
10 bags yellow onions
Step-by-step explanation:
If r is the number of bags of red onions, and y is the number of bags of yellow onions, then:
r + y = 17
4r + 6y = 88
Solve the system of equations using substitution or elimination. Using substitution:
r = 17 − y
4(17 − y) + 6y = 88
68 − 4y + 6y = 88
2y = 20
y = 10
r = 7
The chef received 5 bags of red onions and 12 bags of yellow onions.
The question involves solving a system of linear equations to find the number of bags of red onions and yellow onions the chef received. Let's denote the number of bags of red onions as R and the number of bags of yellow onions as Y. We know that:
Each bag of red onions contains 4 onions.
Each bag of yellow onions contains 6 onions.
The chef got a total of 17 bags.
The chef got a total of 88 onions.
Based on this information, we can set up the following equations:
R + Y = 17
(This represents the total number of bags.)
4R + 6Y = 88
(This represents the total number of onions.)
We can solve this system of equations using substitution or elimination. Let's use substitution. First, we can express Y as 17 - R from the first equation:
Y = 17 - R
Now, we substitute Y in the second equation:
4R + 6(17 - R) = 88
By solving this equation, we find that R = 5 and Y = 12. Therefore, the chef got 5 bags of red onions and 12 bags of yellow onions.
Which two temperatures have a 0 degrees Celsius?
the difference of eight and twice a number
Answer:
8 - 2x
Step-by-step explanation:
Let x be the unknown number
difference is subtraction
8 - 2x
A student participates in a Coke versus Pepsi taste test. She correctly identifies which soda is which four times out of six tries. She claims that this proves that she can reliably tell the difference between the two soft drinks. You have studied statistics and you want to determine the probability of anyone getting at least four right out of six tries just by chance alone. Which of the following would provide an accurate estimate of that probability? Remember, you are trying to prove that four out of six is unusual or not unusual if one truly does not know the taste difference.
A. Repeat this experiment with a very large sample of people and calculate the percentage of people who make four correct guesses out of six tries.
B. Simulate this on the computer with the probability of 50% of guessing the correct soft drink on each try, and calculate the percent of times there are four or more correct guesses out of six trials.
C. No need to run any further tests, since 4 out of 6 is better than half of the time, we would say the student's claim is correct.D. Have the student repeat this experiment many times and calculate the percentage of times she correctly distinguishes between the brands
Answer:
A
Step-by-step explanation:
What is the volume, in cubic in, of a rectangular prism with a height of 19in, a width
of 17in, and a length of 18in?
Answer:
Use (B*H)H
Step-by-step explanation:
17*18*19
First 17*18= 306
Second is 306*19=5814
*PLS HELP ME WITH MY MATH
The volume of the given rectangular prism will be 5814 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
The volume of the prism = length × height × width.
As per the given,
Length = 18 inches
Width = 17 inches
Height = 19 inches
Volume = 18 x 17 x 19 = 5814 inches³
Hence "The volume of the given rectangular prism will be 5814 inches³".
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The Pew Research Center reported in 2018 that 68% of U.S. adults rated "reducing health care costs" as a national priority. This year a survey is conducted with a national sample of 1,505 U.S. adults selected by a combination of landline and cell phone random digit dials. This year's survey finds that 70% of the sample says that "reducing health care costs" is a national priority.
We test the following hypotheses:
H0: The proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is still 0.68.
Ha: The proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is greater than 0.68.
The P-value is 0.045. At a 5% significance level, we would reject the null hypothesis and concluded that the proportion of U.S. adults this year who rate "reducing health care costs" as a national priority is greater than 0.68.
Explain the P-value in the context of this issue.
A P-value of 0.045 suggests that there is a 4.5% chance of observing a sample proportion as extreme as 70% or more, assuming the null hypothesis is true. If the P-value<0.05 (usually considered a threshold), we typically reject the null hypothesis - here, indicating that more than 68% consider health care cost reduction a national priority.
Explanation:In statistics, a P-value is a probability that provides a measure of the evidence against the null hypothesis (H₀). A P-value of 0.045, as given in this instance, indicates that if the null hypothesis were true (i.e., 68% of U.S. adults still consider reducing health care costs a national priority), there is only a 4.5% probability of observing a sample proportion as extreme as 70% or more.
Commonly, a threshold (α) is set at 0.05 or 5%. If the P-value is less than α (which it is in this case, 0.045 < 0.05), we reject the null hypothesis in favor of the alternative hypothesis. Consequently, we conclude there is sufficient evidence to suggest that the proportion of U.S. adults this year who rate 'reducing health care costs' as a national priority is higher than 68%.
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The P-value of 0.045 provides statistically significant evidence to reject the null hypothesis and support the alternative hypothesis that the proportion of U.S. adults who rate 'reducing healthcare costs' as a national priority has increased from the previous 68%.
Explanation:In the context of this issue, the P-value of 0.045 represents the probability of observing a sample proportion as extreme as 70%, or more, given that the null hypothesis is true - the null hypothesis being that the true proportion of U.S. adults who rate 'reducing healthcare costs' as a national priority is 68%.
If the P-value is less than or equal to the significance level (in this case, 5% or 0.05), we reject the null hypothesis. Since 0.045 is indeed less than 0.05, we reject the null hypothesis, supporting the alternative hypothesis that the proportion of U.S. adults who view reducing healthcare costs as a national priority is greater than 68%.
Therefore, the P-value of 0.045 suggests there is statistically significant evidence to conclude that the perception of 'reducing healthcare costs' as a national priority has increased amongst U.S. adults recently.
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Someone ran 2km someone else ran 3,500 meters what would be that combined
Answer:
5,500 meters or 5.5km
Step-by-step explanation:
1 km is = 1000 meter
2km=2000 meters
2000 +3500 =5,5000 meters
Sadie wrote the following on the board find and correct her mistake 2years= 24 weeks
Let f(x)=(3)x−3. Evaluate f(0) without using a calculator.
To evaluate f(0) without using a calculator, simply substitute x with 0 in the function f(x) = 3x - 3 to get f(0) = -3.
Explanation:A mathematical function is a relationship between a set of inputs (domain) and corresponding outputs (range) such that each input is associated with exactly one output. It is a rule or process that assigns a unique value to each input. Functions are fundamental in expressing and analyzing mathematical relationships.
To evaluate f(0) without using a calculator, we can simply replace x with 0 in the given function f(x) = 3x - 3.
Therefore, f(0) = 3(0) - 3 = 0 - 3 = -3.
So, f(0) = -3.
Study the graph of f(x) = 10x. Use the drop-down menus to identify the lines that represent the functions below. p(x) = 10(x + 4) r(x) = 10(x) + 4
Answer:
1 (line B)
2 (line A)
3 (line D)
Step-by-step explanation: We both know I don't have one.
Answer:
b , a , d
Step-by-step explanation:
edg2020
Range of f(x)=-(x-5)^2+9
Answer: (5, -9)
Step-by-step explanation:
Rewrite the equation in term of x and y.
A private and a public university are located in the same city. For the private university, 1042 alumni were surveyed and 655 said that they attended at least one class reunion. For the public university, 796 out of 1318 sampled alumni claimed they have attended at least one class reunion. Is the difference in the sample proportions statistically significant? (Use α=0.05)
Answer:
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of alumni that assist to at least a one class reunion is different for privates university and public university (p-value=0.222).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of alumni that assist to at least a one class reunion is different for privates university and public university.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
where π1: proportion of private university alunmi that have attended at least one class reunion, and π2: proportion of public university alunmi that have attended at least one class reunion.
The significance level is 0.05.
The sample 1 (private), of size n1=1042 has a proportion of p1=0.6286.
[tex]p_1=X_1/n_1=655/1042=0.6286[/tex]
The sample 2 (public), of size n2=1318 has a proportion of p2=0.6039.
[tex]p_2=X_2/n_2=796/1318=0.6039[/tex]
The difference between proportions is (p1-p2)=0.0247.
[tex]p_d=p_1-p_2=0.6286-0.6039=0.0247[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{655+796}{1042+1318}=\dfrac{1451}{2360}=0.6148[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6148*0.3852}{1042}+\dfrac{0.6148*0.3852}{1318}}\\\\\\s_{p1-p2}=\sqrt{0.00023+0.00018}=\sqrt{0.00041}=0.0202[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0247-0}{0.0202}=\dfrac{0.0247}{0.0202}=1.222[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(t>1.222)=0.222[/tex]
As the P-value (0.222) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of alumni that assist to at least a one class reunion is different for privates university and public university.
To determine if the difference in sample proportions is statistically significant, we can perform a hypothesis test.
Explanation:To determine if the difference in sample proportions is statistically significant, we can perform a hypothesis test.
First, we need to state the hypotheses. The null hypothesis (H0) is that there is no difference in the proportions, and the alternative hypothesis (Ha) is that there is a difference in the proportions.Next, we can calculate the standard error of the difference in sample proportions using the formulas: [tex]SE_{\text{diff}} = \sqrt{\left(\frac{p_1(1-p_1)}{n_1}\right) + \left(\frac{p_2(1-p_2)}{n_2}\right)}[/tex]where p1 and p2 are the sample proportions and n1 and n2 are the sample sizes.Then, we can calculate the test statistic using the formula: test_statistic = (p1 - p2) / SE_diffFinally, we can compare the test statistic to the critical value from the standard normal distribution to determine if the difference in sample proportions is statistically significant.In this case, the test statistic is calculated as [tex]\frac{\frac{655}{1042} - \frac{796}{1318}}{\sqrt{\frac{655}{1042}\left(1 - \frac{655}{1042}\right)/1042 + \frac{796}{1318}\left(1 - \frac{796}{1318}\right)/1318}}[/tex] By comparing the test statistic to the critical value at a significance level of 0.05, we can determine if the difference in sample proportions is statistically significant.
Learn more about Hypothesis test on sample proportions here:https://brainly.com/question/30624926
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What is the quotient? Will give brainliest and will report absurd answers.
Answer:
D
Step-by-step explanation:
When dividing fractions, multiply the first number by the reciprocal of the second number
2/5 ÷ 1/3
First, find the reciprocal of the second number: 1/3
To find the reciprocal, flip the numerator (top number) and denominator (bottom number)
1/3-->3/1
Now, multiply 2/5 and 3/1
2/5 * 3/1
Multiply across the numerators and denominators
6/5
Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 444 classical songs, 333 rock songs, and 222 rap songs on it. Chen is going to listen to 360360360 songs.
What is the best prediction for the number of times Chen will listen to a classical song?
Answer:
160160160 times
Step-by-step explanation:
(444/999)360360360=160160160
Answer:
its d
Step-by-step explanation:
its d
Simplify the following expression 1^9
Answer:
1
Step-by-step explanation: