Exam 11: Estimating Means With Confidence

A random sample of 250 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the standard error of the sample mean?

When constructing a confidence interval for the difference in two population means, it is appropriate to use the pooled standard error only when

A 95% confidence interval for the difference in the population proportions of men (group 1) and women (group 2) who exercise regularly, is [-0.06 to +0.10]. Which of the following is not a reasonable conclusion from this confidence interval?

Use the following information for questions: An experiment is conducted with 15 seniors who are taking Spanish at Oak View High School. A randomly selected group of eight students is first tested with a written test and a day later with an oral exam. To avoid order effects, the other seven students are tested in reverse order. The instructor is interested in the difference in grades between the two testing methods. SPSS is used to obtain descriptive statistics for the grades of the two tests. -What are the degrees of freedom for this design?

Which of the following will not result in paired data?

For a randomly selected sample of n = 36 men's heights, it is reported that the standard error of the mean is 0.5 inches. Three of the following statements are true, while one is false. Which statement is false?

Use the following information for questions: For each study, decide if the two samples are independent samples or paired samples. -A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions of students with colds were compared.

The head circumference is measured for a sample of 17 girls and a separate sample of 12 boys. The mean for the girls was 49 cm with a standard deviation of 1.25 cm. The mean for the boys was 50 cm with a standard deviation of 0.95 cm. What is the value of the pooled standard error for the difference in mean head circumference between girls and boys?

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. -Is the following statement about the 95% confidence level true or false? If repeated samples of the same sizes were obtained, we would expect 95% of the resulting intervals to contain the population proportion of lung cancer victims that are non-smokers.

Use the following information for questions: A manufacturer of cell phones is interested in evaluating two alternative existing layout and flow path designs. Design 1 is the current one in use and Design 2 is a new proposed plan. Both designs were implemented for eight consecutive working days and the output of each design was recorded. -What are the degrees of freedom for this paired design analysis?

The confidence level for a confidence interval for a mean is

Use the following information for questions: A manufacturer of cell phones is interested in evaluating two alternative existing layout and flow path designs. Design 1 is the current one in use and Design 2 is a new proposed plan. Both designs were implemented for eight consecutive working days and the output of each design was recorded. -How would a 90% confidence interval for the mean difference in output compare to the 95% confidence interval?

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?" -Based on the output, what value estimates, roughly, the average difference that would be found between the sample mean $\overline{x}$ and the population mean ? in repeated samples of this size?

Use the following information for questions: A manufacturer of cell phones is interested in evaluating two alternative existing layout and flow path designs. Design 1 is the current one in use and Design 2 is a new proposed plan. Both designs were implemented for eight consecutive working days and the output of each design was recorded. -Suppose the sample mean difference in output (Design 2 - Design 1) was -174 phones and the standard error of the mean difference was 28. What is the 95% confidence interval for the population mean difference in output?

Use the following information for questions: An experiment is conducted with 15 seniors who are taking Spanish at Oak View High School. A randomly selected group of eight students is first tested with a written test and a day later with an oral exam. To avoid order effects, the other seven students are tested in reverse order. The instructor is interested in the difference in grades between the two testing methods. SPSS is used to obtain descriptive statistics for the grades of the two tests. -Calculate a 98% confidence interval for the difference in mean grades between the two testing methods.

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. -What is the standard error for the average airborne time?

Use the following information for questions: Spatial perception is measured on a scale from 0 to 10. Two groups of 8^th grade children are tested for spatial perception. The students in group 1 were first given a short course on spatial concepts. The students in group 2 received no such instruction. SPSS was used to calculate descriptive statistics for the two samples. -Calculate a 90% confidence interval for the mean spatial perception score for students without instruction.

The head circumference is measured for 25 girls and their twin sisters. What is the value of the multiplier t* for a 90% confidence interval for the difference in mean head circumference between girl twins?

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. -There is a 95% probability that the population proportion of lung cancer victims that are non-smokers is between 0.10 and 0.15.

A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. Calculate a 99% confidence interval for the mean score on this test.