Question

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APPLIED STATISTICS H. W, #8 Due on: Tuesday, March 26 2019 A radio executive considering a switch in his station's format collects data on the radio preferences of various age groups of listeners. Using the following cross-tabulation, test the null hypothesis that radio format preference does not differ by age group. Age Radio Format Preference Music News-Talk Sports Young Middle Older Adult Age Adult 14 103 41 5 11 A) State the null hypothesis and the Research hypothesis B) Sow all the five steps C Based on the enrollments, use the three by three chi-square to test the null hypothesis that radio format preference does not differ by age group at .05 level of significance. D) What should the researcher conclude from the analysis?

Answer 1

(A)

H0: Null Hypothesis: Radio format preference does not differ by age group

HA: Research Hypothesis: Radio format preference differ by age group

(B) All five steps:

Step 1:Identify X's and Y's:

            Here, X is the age and Y is Radio format preference

Step 2: Calculate the margin summaries

Here, we get the Observed Frequencies as follows:

Radio Format Preference	Young adult	Middle age	Older adult	Total
Music	14	10	3	27
News - Talk	41	5	11	57
Sports	7	9	5	21
Total	62	24	19	105

Step 3: Complete the Contingency Table.

Here, the Expected Frequencies are got as follows:

Radio Format Preference	Young adult	Middle age	Older adult	Total
Music	62X27/105=15.94	6.17	4.89	27
News - Talk	33.66	13.03	10.31	57
Sports	12.40	4.80	3.80	21
Total	62	24	19	105

Step 4: Calculate the observed $\chi ^{2}$ value based on the Contingency Table

Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
14	15.94	0.24
10	6.17	2.38
3	4.89	0.73
41	33.66	1.60
5	13.03	4.95
11	10.31	0.05
7	12.40	2.35
9	4.80	3.68
5	3.80	0.38
Total = $\chi ^{2}$ =		16.34

Step 5 :

Use standard Tables to compare if observed $\chi ^{2}$ to critical $\chi ^{2}$ :

Here,

$\alpha$ = 0.05

ndf = (r - 1) X (c - 1)

    = (3 - 1) X (3 - 1) = 4

From Table, critical value of $\chi ^{2}$ = 9.4877

Since calculated value of $\chi ^{2}$ = 16.34 is greater than critical value of $\chi ^{2}$ = 9.4877, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that Radio format preference does not differ by age group

(C)

Based on the enrollments, the three by three chi square test is used to test the null hypothesis that Radio format preference does not differ by age group at .05 level of significance.

(d)

The researcher should conclude from the analysis that Radio format preference differ by age group