Question

The historical reports from two major networks showed that the mean number of commercials aired during prime time was equal for both networks last year. In order to find out whether they still air the same number of commercials on average or not, random and independent samples of 100 recent prime time airings from both networks have been considered. The first network aired an average of 110.8 commercials during prime with a standard deviation of 5.0. The second network aired 109.2 commercials with a standard deviation of 4.6. Since the sample size is quite large, assume that the population standard deviations 5.0 and 4.6 can be estimated using the sample standard deviations. At the 0.05 level of significance, is there sufficient evidence to support the claim that the average number of commercials aired during prime time by the first station, μ 1 is not equal to the average number of commercials aired during prime time by the second station μ2? Perform a two-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: The alternative hypothesis:H, The type of test statiCooss one (Choose one) V The value of the test statistic: Round to at least three decimal places.) two critical values at the 0.05 level of significance:and Round to at least three decimal places.) Can we support t of The claim that the mean number commercials aired network is not equal to the mean number of commercials aired d second network? during prime time by the first O Yes No uring prime time b y the

Answer 1

To test $H_0:\mu_1 = \mu_2$ against $H_1:\mu_1 \neq \mu_2$

Here

$\bar{x_1} = 110.8, \sigma_1 = 5,n_1=100$

and $\bar{x_2} = 109.2, \sigma_2= 4.6,n_2=100$

The type of test statistic : z statistic

The test statistic can be written as

which under H₀ follows a standard normal distribution.

(1 - 2) m 2 7t

We reject H₀ at 5% level of significance if $|z_{obs}|>z_{0.025}$

Now,

The value of the test statistic $z_{obs}=2.35498$

Critical value $\pm z_{0.025} = \pm 1.95996$

Since , so we reject H₀ at 5% level of significance and we support the claim that the mean number of commercials aired sring prime time by the first network is not equal to the mean number of commercials aired sring prime time by the second network.

ans-> Yes