Question

according to a recent nielsen report, the variance in the number of Tvs that households own is 3. in a random sample of 18 households, the variance in Tvs was 2.5 at level significance =0.10, is there evidence to suggest the standard deviation in Tv's has decreased? ( p-value method)

A. state the null/alternative hypothesis

B. set-up Recipe for the test value and calculate

C. find the p-value. write the inequality

Answer 1

Here, we have to use Chi square test for the population variance or standard deviation.

A. state the null/alternative hypothesis

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: the variance in the number of TVs’ that households own is 3.

Alternative hypothesis: Ha: the variance in the number of TVs’ that households own is less than 3.

H0: σ2 = 3 versus Ha: σ2 < 3

This is a lower tailed test.

B. set-up Recipe for the test value and calculate

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ2

From given data, we have

n = 18

S^2 = 2.5

σ2 = 3

Chi-square =(18 - 1)*2.5/3

Chi-square =14.16667

C. find the p-value. write the inequality

We are given

Level of significance = α = 0.10

df = n – 1

df =17

Critical value = 10.0852

(by using Chi square table or excel)

P-value = 0.3447

(by using Chi square table or excel)

P-value > α = 0.10

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the variance in the number of TVs’ that households own is less than 3.There is not sufficient evidence to suggest the standard deviation in TVs’ has decreased.