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 $12.65 and a standard deviation of $2 for a comparable restaurant meal.

(a)

Choose the 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:	- Select your answer -µ > 13.04µ ≤ 13.04µ < 13.04µ ≥ 13.04Item 1
Ha:	- Select your answer -µ > 13.04µ ≤ 13.04µ < 13.04µ ≥ 13.04Item 2

(b)

Using the sample from the 100 restaurants, what is the p value? If required, round your answer to four decimal places.

(c)

At α = 0.05, what is your conclusion?

We - Select your answer -rejectfail to rejectItem 4  the null hypothesis. We - Select your answer -cancannotItem 5  conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.

need help with B

Answer 1

Solution:

a)

b) Before finding p-value we need to find test statistic,

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

The provided sample mean is Xˉ = 12.65 and the sample standard deviation is s=2, and the sample size is n = 100.

Using test statistic , we will find out p-value,

Excel formula , =TDIST(1.95,99,1) Here we take positive test statistic and DF = 100- 1 = 99

P-value = 0.027

c) Here The p-value is p = 0.027, and since p = 0.027 < 0.05, it is concluded that the null hypothesis is rejected.

Done