Hypothesis Testing for a Proportion and Confidence Interval

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.

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

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).

Which of the following is the critical Z-value for constructing an 80% confidence interval?

• 1.28

• 1.17

• 2.13

• 1.64

• 1.35

If the difference of two proportions (p₁-p₂) shows a confidence interval of (-0.13, 0.32), what would have been our decision from the 2-prop z-test?

• Fail to reject Ha since 0 is in the interval

• Fail to reject Ho since 0 is in the interval

• Reject Ho since 0 is in the interval

• Reject Ha since 0 is in the interval

Kiley has a dime and a nickel, and she wonders if they have the same likelihood of showing heads when they are flipped. She flips each coin 100 times to test if there is a significant difference in the proportion of flips that they each land showing heads.

Which of the following is an appropriate set of hypotheses for Kiley's significance test?

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• 
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• 

Elsie bought a new bowling ball. She suspects that she'll roll a strike in a larger percentage of rolls with her new ball than her old ball. She takes a sample of 50 rolls with each ball to test if she rolls a strike significantly more often with the new ball.

Which of the following is an appropriate set of hypotheses for Elsie's significance test?

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• 
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A study was done to see if the probability of allergies increased if owning a cat. They randomly sampled 58 people who owned a cat and 34 people who did not own a cat to see if they had allergies or not.

Which hypotheses is correct

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