## Related questions with answers

In an article in the *Journal of Advertising*, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent random samples of television ads are taken in the two countries. A random sample of $400$ television ads in the United Kingdom reveals that $142$ use humor, while a random sample of $500$ television ads in the United States reveals that $122$ use humor.

Test the hypotheses you set up in part $a$ by using critical values and by setting $\alpha$ equal to $.10$, $.05$, $.01$, and $.001$. How much evidence is there that the proportions of U.K. and U.S. ads using humor are different?

Solution

VerifiedThe goal of this task is to test the null versus the alternative hypothesis when the values of $\alpha$ are $0.1, 0.05, 0.01$, and $0.001.$ Hypotheses that will help us try to determine is there a difference between the proportion of using the humor in ads in the United Kingdom and the United States, is this a null hypothesis

$H_0: \mu_1-\mu_2 = 0,$

and this alternative hypothesis:

$H_a: \mu_1-\mu_2 \neq 0.$

The null hypothesis tells us that there is no difference in the proportion of using humor in ads between the United Kingdom and the United States. On the other hand, the alternative hypothesis tells us that there is a difference. In this case, using the critical value rule, we will reject the null hypothesis only if the value of $|z|$, where $z$ represents the test statistic, is greater than the value of $z_{\alpha/2}.$

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