Question

The new general manager of a classical music radio station believed that a new playlist would attract listeners from wider range of ages. Two random samples were taken before and after the new playlist was adopted. Information on the ages of the listeners in the sample are summarized below:

Number of listeners Standard Deviation

Old Playlist 20 7.6

New Playlist 17 8.1

Test, at the 10% level of significance, whether the data provide sufficient evidence to conclude that the new playlist has a larger standard deviation than the old playlist?

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H0: σOld2 = σNew2

Alternative hypothesis HA: σOld2 < σNew2

Formulate an analysis plan. For this analysis, the significance level is 0.10.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF1 = n1 - 1 = 20 -1

D.F1 = 19

DF2 = n2 - 1 = 17 -1

D.F2 = 16

Test statistics:-

F = 0.8804

Since the first sample had the smaller standard deviation, this is a left-tailed test.

p value for the F distribution = P(F < 0.8804)

p value for the F distribution = 0.391.

Interpret results. Since the P-value (0.391) is greater than the significance level (0.10), we have to accept the null hypothesis.

From the above test there is insufficient evidence to conclude that new playlist has a larger standard deviation than the old playlist.