Suppose that a random sample of 25 measurements from a norma

Suppose that a random sample of 25 measurements from a normally distributed population gives a sample mean of 13.2 and a sample standard deviation of 4.5.

Use the sample data to test the hypothesis H0: u < 10 versus H1:u > 10 using a = 0.01.

Calculate the p-value for the hypothesis test.

Solution

Suppose that a random sample of 25 measurements from a normally distributed population gives a sample mean of 13.2 and a sample standard deviation of 4.5.

Use the sample data to test the hypothesis H0: u < 10 versus H1:u > 10 using a = 0.01.

Calculate the p-value for the hypothesis test.

This is upper tail test

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

10

Level of Significance

0.01

Sample Size

25

Sample Mean

13.2

Sample Standard Deviation

4.5

Intermediate Calculations

Standard Error of the Mean

0.9000

Degrees of Freedom

24

t Test Statistic

3.5556

Upper-Tail Test

Upper Critical Value

2.4922

p-Value

0.0008

Reject the null hypothesis

Required P value =0.0008