Question

What is the p-value for the following one-sample t-test setup: Recent recommendations suggest 60 minutes of physical activity per day. A sample of 30 adults in a study of cardiovascular risk factors report exercising a mean of 55 minutes per day with a standard deviation of 14 minutes. Based on the sample data, is the physical activity significantly less than recommended? Run the appropriate test at a 5% level of significance.

A. 0.01 < p < 0.025

B. 0.025 < p < 0.05

C. 0.05 < p < 0.10

D. 0.10 < p < 0.20

Answer 1

Given that, sample size (n) = 30

sample mean = 55 minutes and

sample standard deviation = 14 minutes

The null and alternative hypotheses are,

H0 : μ = 60 minutes

Ha : μ < 60 minutes

Test statistic is,

=> Test statistic = t = -1.956

Degrees of freedom = 30 - 1 = 29

Using Excel we find the p-value as follows :

Excel Command : =TDIST (1.956, 29, 1) = 0.0301

=> p-value = 0.0301

Therefore, range for the p-value is : 0.025 < p < 0.05

Answer : B) 0.025 < p < 0.05

Since, p-value is less than 0.05, we reject the null hypothesis.

Note : using t-table also we get the range for p-value is : 0.025 < p-value < 0.05