Question

Sampling voters. Your state representative is planning on supporting a bill legalizing same-sex marriage in your state and wants to estimate the proportion of voters in her district who support this bill. She mails a survey to an SRS of 1300 registered voters in her district, and 800 surveys are returned. In the sample of 800 surveys returned to your state representative, 506 are from female voters.

a) In her district, voter registration records show that 54% of registered voters are female. If the 800 returned surveys are an SRS of registered voters, do you feel that the difference between the proportion of female voters that responded to the survey and the population proportion of 54% can be easily explained by chance variation?

Select the correct hypotheses:

H0:p=0.54H0:p=0.54

H0:p>0.54H0:p>0.54

H0:p≠0.54H0:p≠0.54

H0:p<0.54H0:p<0.54

Ha:p≠0.54Ha:p≠0.54

Ha:p=0.54Ha:p=0.54

Ha:p>0.54Ha:p>0.54

Ha:p<0.54Ha:p<0.54

The sample proportion of females is (round your answer to two decimal places): pˆ=p^=

The test statistic is (round your answer to two decimal places):

The P-value is approximately:

You conclude:

There is overwhelming evidence that the sample is a good representation of the population of the district in terms of sex.

There is overwhelming evidence that the sample does not represent the population of the district in terms of sex.

b) Among the 800 surveys that are returned, 72% support the bill. If women are more likely to support the bill legalizing same-sex marriage than men, what would be the likely direction of the bias in the estimate of the proportion of registered voters who support the bill?

The direction of the bias would be to decrease the proportion in the survey responses of those who favor it.

The direction of the bias would be to increase the proportion in the survey responses of those who favor it.

Answer 1

a) here we will conduct a two tailed test with signiificance level 0.05

since the null hypothesis is rejected There is overwhelming evidence that the sample does not represent the population of the district in terms of sex.

b)The direction of the bias would be to increase the proportion in the survey responses of those who favor it.

Since there are more women then men