Question

A teacher decides to test a hypothesis if the variance population of a sample of pencils is less than 0.6 with given   is 0.01. A random sample of 30 pencils with standard deviation of 0.2 claims that the length of the pencil is approximately normally distributed with a standard deviation is 0.3. Is there enough evidence to support the claim?

Answer 1

Solution

Let the population variance of pencils be denoted by

Here we are to test

The sample size (n) is given as 30

Sample SD (s) is given to be 0.3

The significance level is set at 0.01

The test statistic is obtained as

The test statistic follows distribution with df 29

The critical value is obtained from the Biometrika table as 49.588

As the observed value is less than the critical value, we fail to reject the null hypothesis at 1% level of significance and hence conclude that there is not enough evidence to support the claim of the teacher.