Exam 11: Estimating Means With Confidence

Random samples of 200 men and 200 women were collected and their resting pulse rates were measured, to estimate how much mean resting pulse rates differ for men and women in the population. An analyst mistakenly paired the observations and constructed an approximate 95% confidence interval for the mean difference to be (5 $\pm$ 2×0.2) beats per minute. If the data had been analyzed correctly, finding an approximate 95% confidence interval for the difference in population means, which of the following parts of the interval would be different?

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. -The 90% confidence interval for the difference in average hourly pay (young - middle aged) was found to be (-2.55, 1.43). Based on this interval, what conclusion can we draw about the average hourly pay for these two age groups?

The heights of a sample of n = 18 female college students will be used to create a 98% confidence interval for the mean height of all female college students. What is the correct t* multiplier for this interval?

The WISC scores (similar to IQ test scores) of a sample of n = 20 5^th graders will be used to create a 99% confidence interval for the mean WISC score of all 5^th graders. What is the correct t* multiplier for this interval?

Random samples of 5 Japanese women and 10 Japanese men showed an average life span of 83 years for the women and 77 years for the men. The standard deviation was 2 years for the women and 1 year for the men. Calculate a 95% confidence interval for the difference in average life spans (women $\mu$ men). Assume that the life spans are normally distributed, but do not assume the population variances are equal, and use the conservative "by-hand" estimate for the degrees of freedom.

Use the following information for questions: For a random sample of n = 203 adults in a survey, here is a summary of responses to "How long did you sleep last night?" -Which of the following provides an approximate 95% confidence interval for the mean hours of sleep the previous night in the population represented by the sample?

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. -Explain why this is a paired data design.

A randomly selected sample of n = 51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years, and the standard error of the mean is 1.400. Calculate a 90% confidence interval for the average lifespan for all men in Brazil.

Which of the following helps determine the standard error for a confidence interval for a mean?

For which one of the following situations was a procedure for finding a confidence interval not covered in the textbook?

Use the following information for questions: For a random sample of n = 203 adults in a survey, here is a summary of responses to "How long did you sleep last night?" -What confidence level would be associated with the interval 6.42 - 0.11 as a confidence interval for the population mean $\mu$ ?

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. Calculate a 90% pooled confidence interval for the difference in average amounts spent on textbooks (math majors - English majors).

The cholesterol levels of a random sample of 100 men are measured. The sample mean is 188 and the sample standard deviation is 40. Which of the following provides a 95% confidence interval for the population mean?

Which of the following studies describes a paired data design?

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. -Give an approximate 95% confidence interval for the average left foot length for college men.

Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 145 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. What is the standard error for the difference between the two sample means?

Use the following information for questions: For a randomly selected sample of 20 new mothers in the year 2000, the mean age was 24.6 years. For a randomly selected sample of 10 new mothers in 1970, the mean age was 21.4 years. The difference between the mean ages is 3.2 years, and the standard error of the difference is 1.366. Assume that the ages of new mothers are normally distributed, do not assume the population variances are equal, and use the conservative "by hand" estimate for the degrees of freedom. -Calculate a 99% confidence interval for the difference in population mean ages of new mothers in the two years (year 2000 - year 1970).

A researcher asked random samples of 50 kindergarten teachers and 50 12^th grade teachers how much money they spent out-of-pocket on school supplies in the previous school year, to see if teachers at one grade level spend more than the other. A 95% confidence interval for $\mu$ _K- $\mu$ ₁₂ is $30 to $50. Based on this result, it is reasonable to conclude that

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. -In terms of the notation of this course, what is the correct way to express the "Mean" shown in the output?

A randomly selected sample of 100 students had an average grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean is