# Wwwyorkvilleuca busi 1013 s tatistics for b usiness 9

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BUSI 1013: S TATISTICS FOR B USINESS 9 Two-sample z -interval for p 1 - p 2 Why? To locate the difference between two population proportions p 1 - p 2 . When? Under the same conditions as for the z -test listed above. How: 2 2 2 1 1 1 2 1 ˆ 1 ˆ ˆ 1 ˆ ˆ ˆ n p p n p p z p p c where c z is the critical value from the standard normal distribution corresponding to level C confidence. OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
BUSI 1013: S TATISTICS FOR B USINESS 10 Now, our week assignment: 1. Waiting time at checkout lines for two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2. ( 12 points ) Store 1 (in Seconds) Store 2 (in Seconds) 470 375 394 319 167 266 293 324 187 244 115 178 195 279 400 289 228 342 315 212
195 188 a. What are the null and alternative hypothesis for this research?
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b. What are the sample mean waiting time at checkout lines and the sample standard deviation for the two stores?
c. Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead.
d. Compute the degree of freedom for the test statistic t.
e. Can the chain conclude that the mean waiting time at Store 1 is lower than that of Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
Since t = -0.551 is not less than -1.74 or -1.734, do not reject H 0 The chain cannot conclude that the mean waiting time at Store 1 is lower than that of Store 2 f. Construct a 95% confidence interval for the difference of mean waiting time at checkout lines for the two stores.
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