Exam 11: Estimating Means With Confidence

A prospective study on the relationship between sleep deprivation and heart disease was done by Ayas, et. al. (Arch Intern Med 2003). Women who slept 6 hours a night were compared to women who slept for 8 hours a night (reference group). After adjusting for potential confounding variables like smoking, a 95% confidence interval for the relative risk of heart disease was (0.98, 1.42). Based on this confidence interval, state what the association between sleep deprivation and heart disease is.

Use the following information for questions: A union representative has collected some data on the hourly pay of workers in the area. He is curious to find out if hourly pay actually increases with age. He does not have the actual ages of the workers in his sample, but he does have age group information. For now, he wishes to compare the young workers (18-30 years old) with the middle aged workers (31-45 years old) by calculating a confidence interval for the difference in population mean salaries. -What is the appropriate t* multiplier for a 90% confidence interval estimate?

The amount of time single men and women spend on house work is measured for 15 single women and 20 single men. What are the appropriate degrees of freedom for the multiplier t* for a pooled confidence interval for the difference in mean time spent on housework between single men and women?

Use the following information for questions: Based on a random sample of 41 flights, the average minutes of airborne time for an airline was 106 minutes, with a standard deviation of 5 minutes. -Would a 95% confidence interval for the average airborne time for this airline be wider or narrower than the 90% confidence interval?

A random sample of 40 men drank an average of 20 cups of coffee per week during finals, while a sample of 30 women drank an average of 15 cups of coffee per week. The sample standard deviations were 6 cups for the men and 3 cups for the women. The standard error for the difference between the two sample means is 1.095. Calculate an approximate 95% confidence interval for the difference in average cups of coffee drunk (men -women).

Use the following information for questions: "Sunlight makes everyone feel better." To test this claim, 30 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when it is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.73. After three weeks with the special light they fill in the questionnaire again. The average score this time was 3.13. The standard deviation of the differences was 0.822. -Calculate a 95% confidence interval for the difference in average mood scores (after - before).

Use the following information for questions: For each study, decide if the two samples are independent samples or paired samples. -A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 50 freshmen at a community college.

The multiplier for a confidence interval for one mean or the mean of paired differences depends on

The heights of a random sample of 100 women are recorded. The sample mean is 65.3 inches and the sample standard deviation is 3 inches. Which of the following is an approximate 95% confidence interval for the population mean?

An experiment is conducted with two groups of college students. The 25 students in the treatment group scored an average of 3.7 with a standard deviation of 0.8. The 18 students in the placebo group scored an average of 3.3 with a standard deviation of 1.0. Compare the degrees of freedom from Welch's approximation with the conservative "by-hand" estimate for the degrees of freedom.

Use the following information for questions: Managerial training programs often teach supervisory skills. Are these training programs effective? A company psychologist administers a test to each of 10 supervisors before and after attending such a training program. Higher scores indicate increased supervisory skills. The results are used to estimate the mean improvement in supervisory skills. -Does it appear that the training program is effective? Explain how you came to your decision.

Use the following information for questions: "Sunlight makes everyone feel better." To test this claim, 30 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when it is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.73. After three weeks with the special light they fill in the questionnaire again. The average score this time was 3.13. The standard deviation of the differences was 0.822. -What is the value of the standard error for the difference in average mood score?

A random sample of 30 students spent an average amount of $40.00 on a date, with a standard deviation of $5.00. The standard error of the sample mean is 0.913. Calculate an approximate 95% confidence interval for the average amount spent by all students on a date.

Use the following information for questions: For each study, decide if the two samples are independent samples or paired samples. -A group of 50 students each measured the length of their right arm and the length of their left arm. The average right arm lengths were compared to the average left arm lengths.

A random sample of 60 mathematics majors spent an average of $200.00 for textbooks for a term, with a standard deviation of $22.50. A random sample of 40 English majors spent an average of $180.00 for textbooks that term, with a standard deviation of $18.30. What is the value of the pooled standard error for the difference in mean amount spent?

A random sample of 30 airline flights during a storm had a mean delay of 40 minutes. The standard deviation was 5 minutes, and the standard error of the mean is 0.9129. Calculate a 90% confidence interval for the average delay for all flights during a storm.

Use the following information for questions: Based on a random sample of 41 flights, the average minutes of airborne time for an airline was 106 minutes, with a standard deviation of 5 minutes. -Give a 90% confidence interval for the average airborne time for this airline.

Use the following information for questions: Managerial training programs often teach supervisory skills. Are these training programs effective? A company psychologist administers a test to each of 10 supervisors before and after attending such a training program. Higher scores indicate increased supervisory skills. The results are used to estimate the mean improvement in supervisory skills. -Suppose the mean improvement in supervisory skills was 3 point and the standard deviation of the sampled differences was 2 points. Give the standard error of the sample mean difference.

A cola-tasting experiment is conducted in which 100 people are each given a half-cup of Cola A and a half-cup of Cola B. All 100 participants taste both colas and then rate the taste of each cola on a 0 (horrible) to 50 (tastes great) scale. For each person, a coin is tossed to determine the order of tasting the two colas. To estimate the mean difference between ratings of the two products, what procedure should be used?

Use the following information for questions: Refer to the following statistical summary of the left foot lengths (in centimeters) for a random sample of 76 college men. -Complete the following sentence: In about 95% of all samples of this size from this population, the difference between the sample mean and the population mean would be ____.