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# Hypothesis test for the difference of population means: Paired comparisons

Attached is 2 slides on powerpoint. The 1st slide is the problem and the 2nd slide is the answer format. Answer 3 is completed because it requires the use of a t test with degree of freedom that equals 11.

Attached also is the excel data

1) eg: u=0 or u>0 etc
2) same as 1
4) test statistic
5) criticlal value
6) Yes or No

The owner of a chain of mini-marktes wants to compare the saled performance of two her stores. Store 1 and Store 3. Though the two stores have been comparable in the past, the owner has made several improvements to Store 2 and wishes to see if the improvements have made store 2 more popular than store 1. sales can vary considerably depending on the day of the week and the season of the year, so she decides to elinimate such effects by making sure to record each stores' sales on the same sample of days. After choosing a random sample of 12 days, she records the sales for each store on these days, as shown in table 1.
Based on these data, can the owner conclude, at the 0.01 level of significance, that the mean daily sales of store 2 exceeds that of store 1?

#### Solution Preview

1) Null hypothesis H0: mu_d=0

2) Alternative hypothesis H1: mu_d<0