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.
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 = .62 
(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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