In order to compare the mean length of advertising breaks of two Irish TV networks: the mean length of breaks on network 1, μ 1, and the mean length of breaks on network 2, μ 2, independent random samples of ad-breaks are selected from each network, and their lengths measured in minutes. Descriptive statistics found for each sample of TV ad-breaks are provided in the table below : Group Statistics GROUP n Mean Std. Deviation AdbreakLength network 1 network 2 45 50 6.25 4.48 2.04 2.63 i) Carry out a hypothesis test for a significant difference between the two population means, at significance level α = 0.05. The hypotheses being tested are: H 0: μ 1 - μ 2 = 0 H a: μ 1 - μ 2 ≠ 0. Complete the test by filling in the blanks in the following: An estimate of the difference in population means is. . The standard error is. . The distribution is (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS= . Testing at significance level α = 0.05, the rejection region is: less than. and greater than. (2 dec places). There (is evidence/is no evidence) to reject the null hypothesis, H 0. There (is sufficient/is insufficient) evidence to suggest that there is a difference between the two population means, μ 1 and μ 2. ii) Estimate the difference in population means by calculating a 95% confidence interval. The difference between the population means, the mean of population 1, μ 1, minus the mean of population 2, μ 2, is estimated to be between. and .
In order to compare the mean length of advertising breaks of two Irish TV networks: the mean length of breaks on network 1, μ 1, and the mean length of breaks on network 2, μ 2, independent random samples of ad-breaks are selected from each network, and their lengths measured in minutes.
Group Statistics
GROUP n Mean Std. Deviation
AdbreakLength network 1
network 2 45
50 6.25
4.48 2.04
2.63
i) Carry out a hypothesis test for a significant difference between the two population means, at significance level α = 0.05.
The hypotheses being tested are:
H 0: μ 1 - μ 2 = 0
H a: μ 1 - μ 2 ≠ 0.
Complete the test by filling in the blanks in the following:
An estimate of the difference in population means is. .
The standard error is. .
The distribution is (examples: normal / t12 / chisquare4 / F5,6).
The test statistic has value TS= .
Testing at significance level α = 0.05, the rejection region is:
less than. and greater than. (2 dec places).
There (is evidence/is no evidence) to reject the null hypothesis, H 0.
There (is sufficient/is insufficient) evidence to suggest that there is a difference between the two population means, μ 1 and μ 2.
ii) Estimate the difference in population means by calculating a 95% confidence interval.
The difference between the population means, the mean of population 1, μ 1, minus the mean of population 2, μ 2, is estimated to be between. and .
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