Exam 22: Inferences About Means

You are considering moving to Richmond Hill,and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 50 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

A sociologist develops a test to measure attitudes about public transportation.She wishes to compute a 90% confidence interval for the mean score on this test.It is believed that the standard deviation for these test scores will be 21.How many people should be given the test in order to achieve a margin of error of 10?

80% confidence interval with df = 11

Based on a sample of 32 randomly selected years,a 90% confidence interval for the mean annual precipitation in one city is from 119.1 cm to 125.9 cm

An 80% confidence interval from a sample of size 8

A bank needs information concerning the checking account balances of its local customers.A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29.Find a 98% confidence interval for the true mean checking account balance for local customers.

A manufacturer claims that the mean weight of flour in its 1 kg bags is 1.025 kg.A t-test is performed to determine whether the mean weight is actually less than this.The hypotheses are The mean weight for a sample of 45 bags of flour was 1.011 kg.Suppose that the P-value corresponding to this sample data is 0.001.What does the P-value tell you?

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 21 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 21 people yields a mean cholesterol level of 224 and a standard deviation of 12.Construct a 95% confidence interval.

You are concerned about the high price of gas in your city.You want to determine if the mean price for a litre of gas has exceeded $1.40.

Suppose you have obtained a confidence interval for μ,but wish to obtain a greater degree of precision.Which of the following would result in a narrower confidence interval? I.Increasing the sample size while keeping the confidence level fixed II.Decreasing the sample size while keeping the confidence level fixed III.Increasing the confidence level while keeping the sample size fixed IV.Decreasing the confidence level while keeping the sample size fixed

In the past,the mean battery life for a certain type of flashlight battery has been 9.5 hours.The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean battery life has increased as a result.The hypotheses are: : μ = 9.5 hours : μ > 9.5 hours Explain the result of a Type II error.

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200.They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

Suppose that scores for men on an aptitude test have greater variability than scores for women on the same test.In other words,the population standard deviation is greater for the population of men than for the population of women.Based on a sample of size 50,a 95% confidence interval for the mean score,μ,of all women has a margin of error of 2.2.Which of the following confidence intervals will have a smaller margin of error? I.A 99% confidence interval for the mean score of women.Sample size = 50 II.A 95% confidence interval for the mean score of women.Sample size = 100 III.A 95% confidence interval for the mean score of men.Sample size = 50

A 90% confidence interval from a sample of size 20.

A man on trial is accused of murder in the first degree.The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent.This situation can be modeled as a hypothesis test with the following hypotheses: : The defendant is not guilty. : The defendant is guilty. Explain the result of a Type II error.

P-value for t ≥ 1.76 with 24 degrees of freedom

In 1990,the average duration of long-distance telephone calls originating in one town was 7.2 minutes.A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes.

A scientist in Smallville tested the cholesterol of a random sample of 35 town residents.He constructed the following confidence interval: T-interval for μ: with 99.00% Confidence,188 < μ(Cholesterol)< 206

To determine the mean number of unpopped kernels in your favorite brand of microwave popcorn,you pop a random sample of 50 bags of popcorn and construct of 98% confidence interval of (12.5,15.4).