Waiting time for checkout line at two stores of asupermarket chain were measured for a random sample of customers ateach store. The chain wants to use this data to test the research(alternative) hypothesis that the mean waiting time for checkout atStore 1 is lower than that of Store 2.
Store 1 (in Seconds)
Store 2 (in Seconds)

461
264

384
308

167
266

293
224

187
244

115
178

195
279

280
289

228
253

315
223

205

197

What are the null and alternative hypothesis for thisresearch?

What are the sample mean waiting time for checkoutline and the sample standard deviation for the two stores?

Compute the test statistic t used to test thehypothesis. Note that the population standard deviations are notknown and therefore you cannot use the formula in Section 10.1. Usethe one in Section 10.2 instead.

Compute the degree of freedom for the test statistict.

Can the chain conclude that the mean waiting time forcheckout at Store 1 is lower than that of Store 2? Use thecritical-value approach and ? = 0.05 to conduct the hypothesistest.

Construct a 95% confidence interval for the differenceof mean waiting time for checkout line at the two stores.

To compare prices of two grocery stores in Toronto, arandom sample of items that are sold in both stores were selectedand their price noted in the first weekend of July 2018:

Item
Store A
Store B
Difference (Store A - Store B)

1
1.65
1.99
-0.34

2
8.70
8.49
0.21

3
0.75
0.90
-0.15

4
1.05
0.99
0.06

5
11.30
11.99
-0.69

6
7.70
7.99
-0.29

7
6.55
6.99
-0.44

8
3.70
3.59
0.11

9
8.60
8.99
-0.39

10
3.90
4.29
-0.39

What are the null and alternative hypothesis if wewant to confirm that on average, prices at Store 1 is differentfrom the prices at Store 2, that is, the difference is differentfrom 0?

What are the sample mean difference in prices and thesample standard deviation?

Compute the test statistic t used to test thehypothesis.

Compute the degree of freedom for the test statistict

Can we conclude that on average, prices at Store 1 isdifferent from the prices at Store 2? Use the critical-valueapproach and ? = 0.05 to conduct the hypothesis test.

Use the above data to construct a 95% confidenceinterval for the difference in prices between the two stores.

3. In a completely randomized design, 7 experimentalunits were used for each of the three levels of the factor. (Total:6 marks; 2 marks each)

Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F

Treatment

Error
432076.5

Total
675643.3

Complete the ANOVA table.

Find the critical value at the 0.05 level ofsignificance from the F table for testing whether the populationmeans for the three levels of the factors are different.

Use the critical value approach and ? = 0.05 to testwhether the population means for the three levels of the factorsare the same.