A political strategist believes that 56% of voters in a certain province support his candidate. He then commissions a poll of 800 voters and 53% of them support his candidate. If , is the political
Strategist's belief warranted?
A) Yes, because the test value -1.01 is in the noncritical region.
B) Yes, because the test value -1.88 is in the critical region.
C) No, because the test value -1.88 is in the noncritical region.
D) No, because the test value -1.71 is in the noncritical region.

Question

A political strategist believes that 56% of voters in a certain province support his candidate. He then commissions a poll of 800 voters and 53% of them support his candidate. If  , is the political
Strategist's belief warranted?
A) Yes, because the test value -1.01 is in the noncritical region. 
B) Yes, because the test value -1.88 is in the critical region. 
C) No, because the test value -1.88 is in the noncritical region. 
D) No, because the test value -1.71 is in the noncritical region.

Quizplus · Accepted Answer

To determine whether the political strategist's belief is warranted or not, we need to conduct a hypothesis test. The null hypothesis assumes that the true proportion of voters who support the candidate is equal to the strategist's belief of 56%, while the alternative hypothesis assumes that the true proportion is different from 56%.

H0: p = 0.56
Ha: p ≠ 0.56

We can use the normal distribution to approximate the sampling distribution of the sample proportion. Under the null hypothesis, the test statistic z follows a standard normal distribution.

The test statistic is calculated as:

z = (p̂ - p) / sqrt(p(1-p)/n)

where p̂ is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Plugging in the values, we get:

z = (0.53 - 0.56) / sqrt(0.56(1-0.56)/800)
z = -1.71

The test value of -1.71 is in the noncritical region because it is larger than the critical value of +/-1.96 at the 5% level of significance. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the true proportion of voters who support the candidate is different from 56%.

So, the answer is D because the test value -1.71 is in the noncritical region.

A Political Strategist Believes That 56% of Voters in a Certain