Question

Four runners were randomly sampled and it was found they ran 10, 14, 18, and 18 miles per week. Assuming the population is normally distributed, if we wish to test the claim that the mean running distance is at least 20 miles per week, what conclusion would you reach at the 10% level of significance? Show all the steps of hypothesis testing. You must state your conclusion in terms of the mean running time of runners.

Answer 1

Ans.

Mean of observations, xbar = (10+14+18+18)/ 4 = 15

Standard deviation, s = [Sum of(x - xbar)^2/(4-1)]^0.5 = 3.8297

Sample size, n = 4

Standard error, se = s/n^0.5 = 3.8297/4^0.5 = 1.91485

Hypothesis,

H0: Xbar > = 20, against

H1: Xbar < 20 (Lower tailed test)

tstatistic = (xbar - Xbar)/se = (15-20)/1.91485 = 2.6111706

p value for 3 (=n-1) degrees of freedom = 0.039805 or 3.9805%

As pvalue < 10% (level of significance), so, we reject the null hypothesis. Hence, the mean running time of runners is not significantly atleast 20 miles.