Proportion Confidence Intervals and Hypothesis Testing

What is the appropriate critical value to use for your margin of error if you are constructing a 99% confidence interval for 2 proportions?

109 randomly selected college students were asked, "Did you select your college because it had a reputation as a 'party school' ?" From those 109, 45 responded yes. At the .05 significance level, what is the correct conclusion after conducting the appropriate hypothesis test to determine if less than half of college students chose their college because it had a reputation as a 'party school'?

• P-value is greater than .05, reject Ho and conclude that less than half of students chose their school because it was a party school.

• P-value is greater than .05, reject Ha and conclude that more than half of students chose their school because it was a party school.

• P-value is less than .05, reject Ho and conclude that less than half of students chose their school because it was a party school.

• P-value is greater than .05, fail to reject Ho and conclude that we do not know if less than half of students chose their school because it was a party school.

38 out of 60 randomly selected NJ residents are Yankees fans. 41 out of 70 randomly selected NY residents are Yankees fans. The corresponding 95% confidence interval is (-.1203, .2155). Does this interval indicate that a larger proportion of NJ residents are fans of the Yankees than NY residents?

• Yes, because the positive bound is larger than the negative bound.

• No, because the interval contains both positive and negative values indicating it could go either way.

• No, because the values are less than 95%.

• Yes, because 38/60 (.633) is bigger than 41/70 (.586).

47 students from Lyndhurst HS and 62 students from Rutherford HS were asked how many times a year they go to American Dream mall. The mean and standard deviation for Lyndhurst was 9.27 and 4.8, while the mean and standard deviation for Rutherford was 12.55 and 6.2. Does this provide convincing evidence at the .01 level that Rutherford HS students go to American Dream mall at least 2 more times a year than Lyndhurst HS students? Show ALL of your work in the box and give the FULL explanation!

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A large school district was considering changing the start times to its schools. The change would involve high schools starting later and elementary schools starting earlier. The school district was curious if parents supported this change, so they surveyed separate random samples of parents from both types of school in the district.

The school district wants to determine if the proportion of parents who support the change is significantly different for each type of school. Assume that all conditions have been met.

Which of the following would be an appropriate test statistic for the district's test?

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A political consultant wondered if support for a candidate was significantly different between men and women. The consultant surveyed a random sample of voters.

The consultant wants to test if these results suggest a significant difference in support between men and women. Assume that all conditions have been met.

Which of the following would be an appropriate test statistic for their test?

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Caroline thinks she can flip a coin so it lands showing heads more often with her right hand. She flipped a coin 40 times with each hand. She wants to test whether she gets more heads with her right hand than her left hand. (Assume all conditions have been met.)

Which of the following would be an appropriate test statistic for their test?

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A 98% confidence interval has been constructed: (.073, .211). Which of the following is the margin of error?

• .138

• .069

• .276

• .284

• .142

A 98% confidence interval has been constructed: (.073, .211). Which of the following is point estimate that was used?

• .138

• .069

• .276

• .284

• .142

Suppose a 95% confidence interval (.23, .34) has been constructed to estimate the proportion of fish in a lake that are perch.

Which of the following is the correct interpretation of the confidence level?

• There is a 95% chance the true proportion of fish in the lake that are perch is between .23 and .34.

• 95% of samples will result in a proportion between .23 and .34.

• If several samples were taken and confidence intervals were constructed for each, 95% of those confidence intervals would capture the true proportion of perch in the lake.

• If many fish were selected at random from the lake, between .23 and .34 of them would be perch, 95% of the time.

• 95% of all possible samples that could be taken of the same size, from the same lake, fall with 2 standard deviations of the sample statistic (p-hat).