In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 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%. Which of the following is a conclusion that she may make?

Question

justjm · Answer

How you must approach the hypothesis test:
$\mathbf{i. Parameters}$
Let $\mu$ represent the true population mean of snowfall averages over the next 30-years.
$H_0 : \mu = 86.7~in $
$H_a: /mu≠86.7~in$
$\mathbf{ii. Conditions}$
a. We can safely assume the data is obtained from a random sample
b. We can safely assume that the data set is independent, and that the true population size is greater than 10n, or 40.
c. Although the data set is of only 4 units, we may proceed with extreme caution given that there are no major outliers or skew. The Central Limit Theorem holds true.

Given the conditions are met, we may proceed with a 1-sample mean $z-test$ as the population standard deviation is given.

$\mathbf{iii. Calculations}$
$\mu_o=86.7$
$\sigma = 40.4$
$ L_1 = 115.6, 62.9, 168.5, 135.7$
For $\mu≠86.7$
$z=1.6832$
$p=0.0923, ~α=0.05$
$x̄=120.7,~s=44.2556,~n=4$
$p>a$
$\mathbf{iii. Conclusions}$
Since the p-value is greater than alpha, we fail to reject the null hypothesis. The trend of 86.7 inches will continue.