Question

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

“Miniature Golf with the Stars” will only be renewed if it can be established that more than $12\%$of U.S. adults watch the show. A polling company asks a random sample of $2000$U.S. adults if they watch “Miniature Golf with the Stars.” The network uses the data to perform a test of

$H_0:p=0.12$

$H_a:p>0.12$

where $p$is the true proportion of all U.S. adults who watch the show. Describe a Type $I$error and a Type$II$error in this setting, and give a possible consequence of each.

Short answer

Type $I$error rejects null hypothesis $H_0$, once $H_0$is true.

Type $II$error fails to reject null hypothesis $H_0$, once $H_0$is false.

Step-by-step solution

Given Information

It is given that $n=2000$

$H_0:p=0.12$

$H_1:\mu >0.12$

Explanation

Once null hypothesis $H_0$is true, type I error is rejecting it.

Convincing evidence is present that US adults watching show is $>0.12$if true proportion of US adults who watch show is actually $0.12$

Another consequence is that renewing the show, not sufficient people watch the show will led to loss by television network.

Once $H_0$is false, type II error fails to reject $H_0$.

No convincing evidence is present that true proportion of US adults watching show is $>0.12$, if true proportion of US adults who watch show is actually over $0.12$.

Another consequence is that not renewing the show, sufficient people watch the show will led to missing a chance to make profit by television network.