Question

After many years of teaching, a statistics professor computed the variance of the marks on her final exam and found it to be σ2 = 250. She recently made changes to the way in which the final exam is marked and wondered whether this would result in a reduction in the variance. A random sample of this year’s final exam marks are listed here. Can the professor infer at the 10% significance level that the variance has decreased?

57 92 99 73 62 64 75 70 88 60

Answer 1

It is given that a random sample of final exam marks of a year is listed below.

We need to test whether the population variance was decreased at 10% significance level.

First we compute the sample mean and variance for the given data.

The sample mean is,

The sample variance is,

Null hypothesis,

Alternative hypothesis,

Level of significance,

The test statistics: Chi-square test

Hence, the test statistic value is:

The degrees of freedom is,

The value is,

It is observed that, the value is greater than the given significance level so we fail to reject the null hypothesis and conclude that there is insufficient evidence to conclude that the population variance is decreased.