Math

StatisticsQ&A LibraryA machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 7; H1: μ ≠ 7 H0: p = 7; H1: p < 7 H0: μ = 7; H1: μ < 7 H0: p = 7; H1: p ≠ 7 H0: μ = 7; H1: μ > 7 H0: p = 7; H1: p > 7 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces. There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.Question

A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.2 ounces with a standard deviation of 0.40 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance.

What are we testing in this problem?

single proportion

single mean

(a) What is the level of significance?

State the null and alternate hypotheses.*H*_{0}: μ = 7; *H*_{1}: μ ≠ 7
*H*_{0}: *p* = 7; *H*_{1}: *p* < 7
*H*_{0}: μ = 7; *H*_{1}: μ < 7
*H*_{0}: *p* = 7; *H*_{1}: *p* ≠ 7
*H*_{0}: μ = 7; *H*_{1}: μ > 7
*H*_{0}: *p* = 7; *H*_{1}: *p* > 7

(b) What sampling distribution will you use? What assumptions are you making?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the*P*-value.

*P*-value > 0.500
*P*-value < 0.010

Sketch the sampling distribution and show the area corresponding to the*P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

(e) Interpret your conclusion in the context of the application.

State the null and alternate hypotheses.

(b) What sampling distribution will you use? What assumptions are you making?

The Student's *t*, since we assume that *x* has a normal distribution with unknown σ.The Student's *t*, since *n* is large with unknown σ. The standard normal, since we assume that *x* has a normal distribution with known σ.The standard normal, since we assume that *x* has a normal distribution with unknown σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the

0.250 < *P*-value < 0.500

0.100 < *P*-value < 0.250

0.050 < *P*-value < 0.100

0.010 < *P*-value < 0.050

Sketch the sampling distribution and show the area corresponding to the

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.

There is insufficient evidence at the 0.05 level to conclude that the mean amount of coffee per cup differs from 7 ounces.

1 Rating

Tagged in

Find answers to questions asked by student like you

Q: High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. Afte...

A: The proportion of tagged trout in the lake is, p = 700/2000 = 0.35Let X be the number of tagged trou...

Q: On a test, 95% of the questions are answered correctly. If 57 questions are correct, how many quest...

A: The aim is to find the number of questions on the test.Here, the number of question answered correct...

Q: Let z=a be a positive z score in a standard normal distribution. If the area under z>a is 0.4, th...

A: Standard normal distribution:A normal distribution with mean (µ) 0 and variance (σ2) 1 is called sta...

Q: please answer the whole question (3) Let x be per capita income in thousands of dollars. Let y be t...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Q: a. Which of the six correlations above are statistically significant (i) if you test each correlatio...

A: We have been given alpha = 0.05 which implies that the probability of inferring that there is a cor...

Q: The dose-response effect is best described as A. when similar studies produce similar results B...

A: Introduction:The dose-response effect is a measure of the magnitude of the response in the subjects ...

Q: 10) Two cards are drawn from a standard deck of 52 cards and the first is not replaced before the se...

A: In this question, we have to draw two cards from a deck of 52 cards without replacement. Then we hav...

Q: In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6...

A: The provided details:

Q: What degrees of freedom would younormally expect a t test to have when N1 = 40 and N2 = 55?

A: It is provided that there are two samples of size n1=40 and n2=55.So, this is an example of 'two sam...