Stats review #2

An independent random sample of 200 college football players and 150 college basketball players in a certain state showed that 65% of football players received academic tutors. Which of the following is a 90 percent confidence interval for the difference in the proportion of football players that received tutors and the proportion of basketball players that received tutors for the population of this state?

• (.65 - .58) ± 1.96 √ (0.65) ( .58) ( 1 / 200 + 1 / 150)

• (.65 - .58) ± 1.645 √ (0.65) (0.58) (1 / 200 + 1 / 150)

• (.65 - .58) ± 1.96 √ ((.65) (.35) / 200) + ((.58) (.42) / 150)

• (.65 - .58) ± 1.645 √ ((.65) (.35) / 200) + ((.58) (.42) / 150)

Tags

CCSS.HSS.IC.B.4

Suppose a researcher conducts an experiment to test a hypothesis. If she doubles her sample size, which of the following will increase?

I. The power of the hypothesis test.

II. The effect size of the hypothesis test ( the difference between the true value and the value specified in the null hypothesis).

III. The probability of making a Type II error.

• I. only

• II. only

• III. only

• All of the above

• None of the above

In a sample of 145 cups of coffee, customers rated 37 of them as being served "too hot." Calculate a 95% confidence interval for the true proportion of cups of coffee that customers will feel are served "too hot."

• 36.8% to 37.2%

• 23.5% to 27.5%

• 18% to 33%

• 16% to 35%

• Since the population is not stated to be normal, we cannot use typical techniques to find this interval

Tags

CCSS.HSS.IC.B.4

A survey conducted on 1,000 Canadians found that 700 of them refused to receive the H1N1 vaccination. Construct a 95% confidence interval of the estimated proportion of Canadians who refused to receive the vaccination.

• (0.723, 0.777)

• (0.686, 0.714)

• (0.728, 0.672)

• (0.986, 0.914)

• (0.672, 0.728)

Tags

CCSS.HSS.IC.B.4

If the confidence interval for a population proportion changes from 90% to 98% with all else being equal, then...

• the size of the interval increases by 41%.

• the size of the interval decreases by 9%.

• the size of the interval increases by 9%.

• the size of the interval decreases by 41%.

• None of the above.

Tags

CCSS.HSS.IC.B.4

Suppose you construct a 95% confidence interval from a random sample size of n=20 with a sample mean 100 taken from a population with unknown μ and a known σ = 10, and the interval is fairly wide. Which of the following conditions would not lead to a narrower confidence interval?

• If you decrease your confidence interval.

• If you increased your sample size.

• If the sample size was smaller.

• If the population standard deviation was smaller.

• All of the above would lead to a narrower confidence interval.

Tags

CCSS.HSS.IC.B.4

Other things being equal, which of the following actions will reduce the power of a hypothesis test?

I. Increase sample size

II. Increasing significance level

III. Increasing beta, the probability of a Type II error

• I. only

• II. only

• III. only

• All of the above

• None of the above

A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2011. The average usage was found to be 450 kWh. In a very large study in the March quarter of the previous year, it was found that the standard deviation of the usage was 81 kWh. Assuming the standard deviation us unchanged and that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2011.

• 450 ± 2.756 × (81 / √30)

• 450 ± 2.575 × (9 / √30)

• 450 ± 2.33 × (81 / √30)

• 450 ± 2.575 × (81 / √30)

• None of the above

Tags

CCSS.HSS.IC.B.4

Null and alternative hypothesis are statements about:

• population parameters

• sample parameters

• sample statistics

• it depends - sometimes population parameters and sometimes sample statistics

A professor sampled 46 students from a large university to obtain a 95% confidence interval for the proportion of students in favor of raising ASB fees. The interval was ( .356, .397 ). If the professor had used a 90% confidence interval instead, the confidence interval would have been...

• Wider and would have a smaller chance of missing the true proportion.

• Narrower and would have a larger chance of missing the true proportion.

• Narrower and would have a smaller chance of missing the true proportion.

• Wider and would have a larger chance of missing the true proportion.

• Wider, but the chance of missing the true proportion cannot be determined.

Tags

CCSS.HSS.IC.B.4