You may need to use the appropriate technology to answer this question. Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04.† A sample of 100 neighborhood restaurants showed a mean price of $12.73 and a standard deviation of $2 for a comparable restaurant meal. (a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home. H0: μ ≤ 13.04 Ha: μ > 13.04 H0: μ > 13.04 Ha: μ ≤ 13.04 H0: μ ≥ 13.04 Ha: μ < 13.04 H0: μ = 13.04 Ha: μ ≠ 13.04 H0: μ < 13.04 Ha: μ ≥ 13.04 (b) Using the sample from the 100 restaurants, what is the test statistic? Using the sample from the 100 restaurants, what is the p-value? (Round your answer to four decimal places.) p-value = (c) At α = 0.05, what is your conclusion? Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. (d) Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. H0: μ ≤ 13.04 Ha: μ > 13.04 H0: μ > 13.04 Ha: μ ≤ 13.04 H0: μ ≥ 13.04 Ha: μ < 13.04 H0: μ = 13.04 Ha: μ ≠ 13.04 H0: μ < 13.04 Ha: μ ≥ 13.04 Find the value of the test statistic. State the critical values for the rejection rule. Use α = 0.05. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.
You may need to use the appropriate technology to answer this question. Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04.† A sample of 100 neighborhood restaurants showed a mean price of $12.73 and a standard deviation of $2 for a comparable restaurant meal. (a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home. H0: μ ≤ 13.04 Ha: μ > 13.04 H0: μ > 13.04 Ha: μ ≤ 13.04 H0: μ ≥ 13.04 Ha: μ < 13.04 H0: μ = 13.04 Ha: μ ≠ 13.04 H0: μ < 13.04 Ha: μ ≥ 13.04 (b) Using the sample from the 100 restaurants, what is the test statistic? Using the sample from the 100 restaurants, what is the p-value? (Round your answer to four decimal places.) p-value = (c) At α = 0.05, what is your conclusion? Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. (d) Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. H0: μ ≤ 13.04 Ha: μ > 13.04 H0: μ > 13.04 Ha: μ ≤ 13.04 H0: μ ≥ 13.04 Ha: μ < 13.04 H0: μ = 13.04 Ha: μ ≠ 13.04 H0: μ < 13.04 Ha: μ ≥ 13.04 Find the value of the test statistic. State the critical values for the rejection rule. Use α = 0.05. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥ State your conclusion. Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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You may need to use the appropriate technology to answer this question.
Which is cheaper: eating out or dining in? The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04.† A sample of 100 neighborhood restaurants showed a mean price of $12.73 and a standard deviation of $2 for a comparable restaurant meal.
(a)
Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean cost of a restaurant meal is less than fixing a comparable meal at home.
H0: μ ≤ 13.04
Ha: μ > 13.04
H0: μ > 13.04
Ha: μ ≤ 13.04
H0: μ ≥ 13.04
Ha: μ < 13.04
H0: μ = 13.04
Ha: μ ≠ 13.04
H0: μ < 13.04
Ha: μ ≥ 13.04
(b)
Using the sample from the 100 restaurants, what is the test statistic?
Using the sample from the 100 restaurants, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c)
At
α = 0.05,
what is your conclusion?Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.
(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses.
H0: μ ≤ 13.04
Ha: μ > 13.04
H0: μ > 13.04
Ha: μ ≤ 13.04
H0: μ ≥ 13.04
Ha: μ < 13.04
H0: μ = 13.04
Ha: μ ≠ 13.04
H0: μ < 13.04
Ha: μ ≥ 13.04
Find the value of the test statistic.
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistic≤test statistic≥
State your conclusion.
Do not reject H0. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject H0. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject H0. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.
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