Question

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping that it will keep the disapproval rate below 17%. They will use a follow-up poll to assess the ad's effectiveness.Which of these are the null and alternative hypotheses you would use to test this situation?a. H_0: p < 0.17 and H_A: p = 0.17b. H_0: p > 0.17 and H_A: p < 0.17c. H_0: p = 0.17 and H_A: p > 0.17d. H_0: p = 0.17 and H_A: p < 0.17d. H_0: p > 0.17 and H_A: p = 0.17

Answer 1

Answer:

For this case we first define the parameter of interest p as the disapproval rate, we know that they want to keep this rate below and specified value of 17% or equivalent to $p<0.17$, since that's what they want to test needs to be on the alternative hypothesis, and the complement in the null hypothesis. So the system of hypothesis for this case would be:

Null hypothesis:  $p =0.17$

Alternative hypothesis: $p<0.17$

And the best option is:

d. H_0: p = 0.17 and H_A: p < 0.17

Step-by-step explanation:

For this case we first define the parameter of interest p as the disapproval rate, we know that they want to keep this rate below and specified value of 17% or equivalent to $p<0.17$, since that's what they want to test needs to be on the alternative hypothesis, and the complement in the null hypothesis. So the system of hypothesis for this case would be:

Null hypothesis:  $p =0.17$

Alternative hypothesis: $p<0.17$

And the best option is:

d. H_0: p = 0.17 and H_A: p < 0.17