In Juneau, Alaska, the 30 -year annual snowfall average is 86 point 7 inches with a standard deviation of 40 point 4 inches. The last four years saw an average annual snowfall of 115 point 7 inches, 62 point 9 inches, 168 point 5 inches, and 135 point 7 inches. Hia performs a hypothesis test on this data to determine if the next 30 -year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5 percent Which of the following is a conclusion that she may make?
Answer
A
The z -statistic is 1 point 4 4 , so the null hypothesis cannot be rejected.
B
The z -statistic is 4 point 6 , so the null hypothesis should be rejected.
C
The z -statistic is 1 point 8 5 , so the null hypothesis should be rejected.
D
The z -statistic is 1 point 6 8 , so the null hypothesis cannot be rejected.
Explanation
The four-year sample mean is (115.7 + 62.9 + 168.5 + 135.7) / 4 = 120.7 inches. The standard error is 40.4 / √4 = 20.2 inches, so the z-statistic is (120.7 − 86.7) / 20.2 ≈ 1.68. For a two-sided test at the 5% significance level, the critical values are about −1.96 and 1.96; since 1.68 is within that range, she cannot reject the null hypothesis. Thus, choice D is correct.
AI-written and checked against the verified answer.