Question

A poll found that in a random sample of 1000 American adults, 710 indicated that they oppose the reinstatement of a military draft. Is there convincing evidence that the proportion of American adults who oppose reinstatement of the draft is greater than 0.7? Use a significance level of 0.05. (Round your test statistic to two decimal places and your P-value to four decimal places.)

Answer 1

To test if the proportion of American adults who oppose reinstatement of the draft is greater than 0.7, we can conduct a hypothesis test and calculate the test statistic and p-value.

Step-by-step explanation:

To determine whether the proportion of American adults who oppose reinstatement of the draft is greater than 0.7, we can conduct a hypothesis test. The null hypothesis (H0) would be that the proportion is equal to or less than 0.7, while the alternative hypothesis (Ha) would be that the proportion is greater than 0.7.

Next, we calculate the test statistic and the p-value. The test statistic can be calculated using the formula: test statistic = (sample proportion - hypothesized proportion) / standard error of the sample proportion.

Using the given information, we can calculate the test statistic and find its corresponding p-value to make a final decision.

Answer 2

-Accept
`H_o`

-There is no sufficient evidence to back the claim that the proportion of American adults who oppose reinstatement of the draft is greater than 0.7

Step-by-step explanation:

-We state our hypotheses as:

`H_o:p=0.7\\\\\\H_a:p>0.7`

#We the calculate the proportion to be studied using the formula:

`\hat p=(x)/(n)\\\\=(710)/(1000)\\\\=0.71`

-The z-value from this proportion is calculated as follows:

`z=\frac{\hat p-p}{\sqrt{(p(1-p))/(n)}}\\\\=\frac{0.71-0.7}{\sqrt{(0.7*0.3)/(1000)}}\\\\\\=0.6901`

#We compare this z-value to the z-value at 95% confidence level:

`z_(0.025)=1.645\\\\0.6901<1.645`

Hence, Accept the null hypothesis.

-There is no sufficient evidence to back the claim that the proportion of American adults who oppose reinstatement of the draft is greater than 0.7