Question

QUESTION 1

1. 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

2. 
   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____________ .

1. Based on the analysis carried out in the last question, describe the relationship between the two population means,select one of the following options..

	a.	The average length of advertising breaks sampled from network 1 are significantly shorter than the average length of advertising breaks sampled on network 2.
	b.	There is no significant difference between the average length of advertising breaks on network 1 and the average length of advertising breaks on network 2.
	c.	The average length of advertising breaks sampled from network 1 are significantly longer than the average length of advertising breaks sampled from network 2.
	d.	The average length of advertising breaks on network 1 are significantly shorter than the average length of advertising breaks on network 2.
	e.	There is no significant difference between the average length of advertising breaks sampled from network 1 and the average length of advertising breaks sampled from network 2.
	f.	The average length of advertising breaks on network 1 are significantly longer than the average length of advertising breaks on network 2

Were any assumptions required in order for this inference to be valid?

	a.	Yes, the sample of network 1 ad-breaks must be independent of the sample of network 2 ad-breaks. Each population must be normally distributed, i.e. the population of all ad-breaks shown on network 1 have lengths that must be normally distributed and the population of all ad-breaks shown on network 2 have lengths that must be normally distributed.
	b.	Yes, the sample of network 1 ad-breaks must be independent of the sample of network 2 ad-breaks. The Central Limit Theorem applies, which states the sampling distribution is normal for any population distributions.
	c.	No. The Central Limit Theorem applies, which states the sampling distribution is normal for any population distributions.
	d.	Yes , each population must be normally distributed, i.e. the population of all ad-breaks shown on network 1 have lengths that must be normally distributed and the population of all ad-breaks shown on network 2 have lengths that must be normally distributed.

Answer 1