Confidence Intervals and Hypothesis Testing

A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his classes. After collecting data from a random sample of his students, the professor tested the hypothesis H0: μM = μW against the alternative HA: μM ≠ μW. The P-value for the test was 0.003. Which is true?

• It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women.

• There is a 0.3% chance that the mean ages for the men and women are equal.

• There is a 99.7% chance that another sample will give these same results.

• There is a 0.3% chance that another sample will give these same results.

• There is a 0.3% chance that the mean ages for the men and women are different.

Researchers claim that a blue background enhances creativity based on the average scores below. Test the claim at a 1% significance level.

• P = .0021

  We are more creative with blue.

• P = 0.9979

  We are more creative with blue.

• P = .0021

  We are more creative with red.

• P = 0.9979

  There appears to be no difference.

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery. What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college. Find the critical value.

• 0.90

• 1.155

• 1.645

• ±1.645

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size

• decreasing the confidence level, decreasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• Yes

• No

• Not enough information

• I have no idea what you're asking of me

A 90% confidence interval for the mean speed driven by cars on Due West Road is given by (21, 45). What was the sample mean of this study?

• 12

• 24

• 33

• None of these.