Answered: Which is cheaper: eating out or dining…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

H₀: μ ≤ 13.04

H_a: μ > 13.04

H₀: μ > 13.04

H_a: μ ≤ 13.04

H₀: μ ≥ 13.04

H_a: μ < 13.04

H₀: μ = 13.04

H_a: μ ≠ 13.04

H₀: μ < 13.04

H_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)

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

H_a: μ > 13.04

H₀: μ > 13.04

H_a: μ ≤ 13.04

H₀: μ ≥ 13.04

H_a: μ < 13.04

H₀: μ = 13.04

H_a: μ ≠ 13.04

H₀: μ < 13.04

H_a: 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.

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