Question

The 2012 general Social Survey asked a large number of people how much time they spent watching TVeach day. The mean number of hours was 3.09 with a standard deviation of 2.83. Assume that in a sampleof 45 teenagers, the sample standard deviation of daily TV time is 4.1 hours, and that the population ofTV watching times is normally distributed. Can you conclude that the population standard deviation ofTV watching times for teenagers differs from 2.83? Use theα= 0.10 level of significance.

Answer 1

Null Hypothesis H0: Population standard deviation ofTV watching times for teenagers is equal to 2.83.

Alternative Hypothesis H1: Population standard deviation ofTV watching times for teenagers differs from 2.83.

We will use Chi-Square-tests for standard deviation since the original population be normally distributed.

Test statistic, = (n - 1) s² /

= (45 - 1) * 4.1² / 2.83²

= 92.35226

Degree of freedom = n - 1 = 45 - 1 = 44

P-value is P( > 92.35, df = 44) = 0.00003

Since p-value is less than 0.10 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that population standard deviation ofTV watching times for teenagers differs from 2.83