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?

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).

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.

When conducting a hypothesis test and your p-value is greater than your significance level, what is the appropriate conclusion to make?

• Reject Ha

• Accept Ho

• Reject Ho

• Fail to Reject Ho

9 out of 25 students bring their lunch to school. Construct a 90% Confidence Interval for the proportion of students who bring their lunch to school.

Identify the variable

• .36

• Z

• 25

• q

• .64

• p

• 1.645

• n

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

At the State Qualifier Cross Country Meet, 45 out of 150 runners ran under 17 minutes. Construct a 99% Confidence Interval for the proportion of runners that run under 17 minutes. Identify the variables

• 2.58

• n

• 150

• Z

• .7

• p

• .3

• q

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 95 percent confidence interval of the form p̂ ±E will be used to obtain an estimate for an unknown population proportion p. If p̂ is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08?

• 25

• 100

• 175

• 250

• 625