Question

HyVee is redesigning the check out lanes in it's supermarkets and is considering two designs. Tests on customer checkout times conducted at two stores -- the older stores in Iowa versus the new stores in Illinois -- resulted in the following data: Use Table 1. (Note: the automated question following this one will ask you confidence interval questions for this same data, so jot down your work.) Old Iowa stores New Illinois stores    x−1x−1 = 4.1 minutes    x−2x−2 = 3.4 minutes   n1 = 120   σ = 2.2 minutes   n2 = 100   σ = 1.5 minutes Set up the hypotheses to test whether the check out times at the old Iowa stores is higher than that of the newer Illinois stores. H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 Calculate the value of the test statistic and its p-value. At the 10% significance level, what is the conclusion? Reject H0. Accept H0. You can't answer based on the data. Both a and b. d. At the 10% significance level, use the critical value approach for the conclusion. Do not reject H0 since the value of the test statistic is more than 1.28. Do not reject H0 since the value of the test statistic is more than 1.645. Reject H0 since the value of the test statistic is more than 1.28. Reject H0 since the value of the test statistic is more than 1.645. Now provide confidence interval information from the previous question. Specifically: a.    What is the value of the point estimate of the difference between the two population means? b.    What is the margin of error at 90% confidence?         (± what value; please provide to 4 decimals; e.g. "0.1234") c.    With that margin of error, what is the low number in the confidence interval? d.    With that margin of error, what is the high number in the confidence interval?

Answer 1

H0: < 0

H1: > 0

The test statistic z = ()/

                              = (4.1 - 3.4)/sqrt((2.2)^2/120 + (1.5)^2/100)

                              = 2.79

P-value = P(Z > 2.79)

             = 1 - P(Z < 2.79)

             = 1 - 0.9974

             = 0.0026

Since the P-value is less than the significance level(0.0026 < 0.10), so we should reject the null hypothesis.

Reject H₀.

d) At 10% significance level, the critical value is z_0.9 = 1.28

Reject H0 since the value of the test statistic is more than 1.28.

a) = 4.1 - 3.4 = 0.7

b) At 90% confidence interval the critical value is z_0.05 = 1.645

Margin of error = z_0.05 *

                         = 1.645 * sqrt((2.2)^2/120 + (1.5)^2/100)

                         = 0.4123

C) Lower limit = () - E

                       = 0.7 - 0.4123

                       = 0.2877

d) Upper limit = () - E

                       = 0.7 + 0.4123

                       = 1.1123