Question

Please SHOW YOUR Calculations and formulas in Excel

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 neighboring restaurants showed a mean price of $12.75 and a standard deviation of $2 for a comparable restaurant meal.

1) Develop appropriate hypothesis 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.

2) Using the sample from 100 restaurants, what is the p value?

3) At a level of significance of 5%, what is your conclusion?

Answer 1

To Test :-

H0 :- µ >= 13.04
H1 :- µ < 13.04

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 12.75 - 13.04 ) / ( 2 / √(100) )
t = -1.45

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
t(α, n-1) = t(0.05 , 100-1) = 1.66
t > -t(α, n-1) = -1.45 > - 1.66
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.45 ) = 0.0751
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0751 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the mean cost of a restaurant meal is less than fixing a comparable meal at home.

Excel formula to find P value  T.DIST( -1.45 , (100 -1) )