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.

# 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 23PFA

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(PLEASE JUST ANSWER PART D)

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.

H

_{0}: μ ≤ 13.04H

_{a}: μ > 13.04H

_{0}: μ > 13.04H

_{a}: μ ≤ 13.04H

_{0}: μ ≥ 13.04H

_{a}: μ < 13.04H

_{0}: μ = 13.04H

_{a}: μ ≠ 13.04H

_{0}: μ < 13.04H

_{a}: 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 = .62

(c)

At

α = 0.05,

what is your conclusion?Do not reject

*H*_{0}. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject*H*_{0}. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject*H*_{0}. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject*H*_{0}. 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.

H

_{0}: μ ≤ 13.04H

_{a}: μ > 13.04H

_{0}: μ > 13.04H

_{a}: μ ≤ 13.04H

_{0}: μ ≥ 13.04H

_{a}: μ < 13.04H

_{0}: μ = 13.04H

_{a}: μ ≠ 13.04H

_{0}: μ < 13.04H

_{a}: μ ≥ 13.04Find 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.

*H*

_{0}. We can conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Reject

*H*

_{0}. We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home. Reject

*H*

_{0}. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.Do not reject

*H*

_{0}. We cannot conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.

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