Exam 11: Estimating Means With Confidence

An experiment is conducted with two groups of 25 college students. The treatment group scored an average of 3.67 with a standard deviation of 0.86. The placebo group scored an average of 3.29 with a standard deviation of 0.97. Calculate a 95% pooled confidence interval for the difference in means between the treatment and the placebo.

In a random sample of 100 students, the change in hours of sleep for each student during and after finals week were compared. Are the samples of students' sleep during finals and after finals independent samples or paired samples?

Which one of the following ways of collecting data would not result in paired data?

Which one of the following ways of collecting data would result in two independent samples?

A random sample of 100 students had a mean grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean in this case is 0.02. Calculate an approximate 95% confidence interval for the mean GPA for all students.

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. A group of 9^th grade students are tested for spatial perception. SPSS was used to calculate descriptive statistics of the spatial perception scores in the sample. -In terms of the notation of this course, what is the correct way to express the value 0.428 in the output?

A random sample of 60 mathematics majors spent an average of $200.00 for textbooks for a term, while a random sample of 40 literature majors spent an average of $180.00 for textbooks that term. The standard deviation for each sample was $20.00. The standard error for the difference between the two sample means is 4.082. Calculate an approximate 95% confidence interval for the difference in average amounts spent on textbooks (math majors - literature majors).

A randomly selected 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

The head circumference is measured for a sample of 15 girls and a separate sample of 15 boys. What is the correct combination of degrees of freedom and the value of the multiplier t* for a 90% confidence interval for the difference in mean head circumference between girls and boys?

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 had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.

The amount of time the husband and the wife spend on house work is measured for 15 women and their 15 husbands. What are the appropriate degrees of freedom for the multiplier t* for a confidence interval for the difference in mean time spent on housework between husbands and wives?

Reaction time is measured in a driving simulator for a random sample of 16 year-old boys (n = 12, $\overline{x}$ = 4.5,s = 1.1) and a random sample of 24 year-old young men (n = 9, $\overline{x}$ = 2.9, s = 1.3). Calculate a 99% pooled confidence interval for the difference in mean reaction time (16 year-olds - 24 year-olds).

Use the following information for questions: As the number of men with lung cancer declines, the American Cancer Society estimates that 73,020 women will die in the United States of lung cancer this year, more than those who will die from breast, ovarian and uterine cancers combined. While no national studies have yet been done, many lung cancer specialists say they are seeing a disturbing trend of more and more non-smoking women with the disease. Based on one study, it is estimated that 10 to 15 percent of lung cancer victims are non-smokers. Suppose the range from 10 to 15 percent actually represents a 95% confidence interval. -What was the proportion of lung cancer victims in the sample that were non-smokers?

In a random sample of 100 students (60 women and 40 men), the average hours of sleep during finals week were compared. Are the samples of men and women independent samples or paired samples?

A study on the relationship between vertex baldness and heart attacks in men reported that "For any vertex baldness [compared with no baldness], the age-adjusted relative risk [of heart attack] was 1.4 (95% CI, 1.2 to 1.9)." Based on this, it can reasonably (with 95% confidence) be concluded that

Explain what is wrong with the following statement: A t-interval is a confidence interval estimate of a sample mean.

A randomly selected sample of n =51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years. Calculate a 98% confidence interval for the average lifespan for all men in Brazil.

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. -How would the 99% confidence interval for the difference in average hourly pay compare to 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

A 95% confidence interval for the difference between the mean handspans of men and the mean handspans of women is determined to be 2.7 centimeters to 3.3 centimeters. Which of the following statements is the best interpretation of this interval?