# 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.

Question
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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,
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≥
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.