1) Ho: m = 48.98

Ha: m ¹ 48.98

Reject Ho if Z < -2.24 or > 2.24 (Note that we have 1.25% in each tail, indicating that there is 48.75% between 0 and the critical value. Working backward through the Z table gives the upper critical value of 2.24)

Z = (52.57 – 48.98)/(10.23/sqrt(50)) = 2.48

Reject Ho.

Conclude there is a significant difference in average sales between the online and physical stores.

2) Lower limit = 52.57 – 2.24(10.23)/sqrt(50) = 52.57 – 3.24 = 49.33

Upper limit = 52.57 + 3.24 = 55.81

49.33 < m < 55.81

3) Yes. Since the hypothesis mean of 49.98 falls outside the 97.5% confidence interval, we reject Ho at a 2.5% level of significance.

4) P-value = 2P(Z > 2.48); P(Z > 2.48) = 0.5 – 0.4934 = 0.0066; P-value = 2(0.0066) = 0.0132 = 1.32%

5) Yes. Since the p-value < 2.5%, we reject Ho.

6) Since the p-value falls between 1% and 10%, the results are inconclusive under the general rule of thumb.