Question

In: Statistics and Probability

Below is the the number of hours of TV watched by boys and girls per week....

Below is the the number of hours of TV watched by boys and girls per week. Using the data on the number of hours of TV viewing, test the hypothesis that the number of hours of TV watched by girls is less than 7.4 hours per week at a 2% significance level.

Determine the critical values that divide the rejection and nonrejection regions

Observation Number of hours of TV viewed by Boy Number of hours of TV viewed by Girl
1 8 10
2 7 10
3 8 10
4 11 8
5 8 9
6 7 11
7 9 8
8 9 9
9 9 10
10 12 10
11 12 8
12 11 12
13 8 8
14 12 8
15 9 7
16 9 6
17 10 11
18 9 8
19 12 10
20 8 16
21 11 8
22 10 7
23 8 10
24 9 9
25 11 9
26 9 9
27 7 6
28 14 9
29 6 12
30 8 11
31 10 9
32 9 10
33 8 9
34 5 10
35 6 11
36 11 7
37 8 5
38 14 8
39 6 10
40 8 8
41 12 9
42 8 10
43 10 10
44 9 10
45 9 7
46 10 9
47 6 6
48 9 12
49 13 7
50 8 8

Solutions

Expert Solution

  • Hypothesis to be tested:

Vs

The population average time of girls watching T.V.

  • Test Statistics:

    where,
    sample mean
    s: sample s.d.
    n: sample size
  • Test Criteria:
    We reject H0 at level of significance iff-

    where,
    is the percentile value of the "t-distribution" with n-1 df.
  • Calculation:
    9.08
    s:1.9042
    n:50
    T=6.2385
  • Critical Value:

  • Conclusion:
    As here, , so we fail to reject the Null Hypothesis at 0.02 level of significance and conclude on the basis of given data that the number of hours of TV watched by girls is not less than 7.4 hours per week at a 2% significance level.

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