Question

The mean cost of the ingredients of a chicken permesan meal bought at the grocery store is $15. Prices from a sample of 50 restaurants for a comparable meal is shown in spreadsheet PRICES. At an alpha level of .05, can we say that eating chicken parmensan at a restaurant is cheaper? Formulate your hypotheses and solve the problem.

spreadsheet 12.7 12.31 13.51 13.97 9.24 11.4 13.73 13.47 11.62 11.69 14.32 12.42 18.49 11.66 16.59 14.62 14.77 14.06 14.66 9.22 12.64 17.25 11.31 12.96 16.2 12.65 11.11 11.46 15.05 13.56 13.5 13.29 16.27 14.73 14.18 14.43 13.35 12.08 11.64 10.81 12.59 14.83 13.16 9.75 12.16 10.75 16.83 11.7 14.44 9.68

Answer 1

First, we need to find the sample mean and sample standard deviation using the EXCEL function

for mean, using function AVERAGE, we get mean =13.18

for sample standard deviation, using function STDEV.S, we get s = 2.06

Null hypothesis:

Alternate hypothesis:_

we have to use t distribution because population standard deviation is not given

Alpha level is 0.05

Calculation for t statistics

t =

setting the value

we get

t =  

Using the student's t distribution for the calculated t value of -6.25 with degree of freedom = 50-1 = 49, we get the p value = 0.0000

So, it is clear that p value is less than 0.05

Thus, we can reject the null hypothesis and we can conclude that we have enough evidence to support the claim that the eating chicken parmensan at a restaurant is cheaper