Question

Kim is moving to a new winter wonderland and hypothesizes that it snows on average 12 inches in December. She collected data in 25 other cities and found that on average it snows 8.5 inches in those cities with a standard deviation of 1.2 inches. Test the hypothesis within 1.96 standard errors of the mean. Explain.

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 12 versus H_a: µ ≠ 12

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 12

Xbar = 8.5

S = 1.2

n = 25

α = 0.05

Critical value = 1.96

(Given in the problem)

t = (Xbar - µ)/[S/sqrt(n)]

t = (8.5 - 12)/[1.2/sqrt(25)]

t = -14.5833

P-value = 0.0000

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that it snows on average 12 inches in December.