Exam 21: The Role of Confidence Intervals in Research

In practice the population standard deviation, which appears in the formula for the standard error of the mean, is not known.Statisticians replace it with the _______________, computed from the data.

For Questions , use the following narrative Narrative: Classes 1 and 2 Suppose a 95% confidence interval for the difference in test scores between Class 1 and Class 2 (in that order) is the following: 9 +/− 2.These results were based on independent samples of size 100 from each class. -{Classes 1 and 2 narrative} What can you conclude?

For Questions , use the following narrative Narrative: Side effects Suppose in a large study investigating side effects of a new drug, it was found that the relative risk of having bad side effects from the new drug (compared to placebo) is 1.3 (with a 95% confidence interval of 1.1 to 1.8).This compares to the relative risk of having bad side effects from the standard drug (compared to placebo), which was found to be 3.4 (with a 95% confidence interval of 1.7 to 7.0), based on large sample results. -{Side effects narrative} These confidence intervals are not in the usual format of 'sample value plus or minus the margin of error' that we have seen.Explain how we can tell this.

Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 - species #2), and your interval is -3.6 to 61.6 ounces.What can you conclude?

Which of the following statements is not true regarding a 95% confidence interval for the mean of a population?

For Questions , use the following narrative Narrative: Male weight loss Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13.4 and 18.3 pounds.These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. -{Male weight loss narrative} Suppose an individual from this population wants to join this diet program, and wants to know how much weight he can expect to lose.What can you say, given the results above?

You can determine confidence intervals for individual means or for the difference in two means (for large, independent samples) as long as you are given these three things: the means, the standard deviations, and the __________.

For Questions , use the following narrative Narrative: Male weight loss Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13.4 and 18.3 pounds.These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. -{Male weight loss narrative} What is the margin of error?

Suppose a new drug treatment for headaches is compared to placebo in a two independent group matched-pairs study (measuring difference in pain levels before and after for the placebo group and for the drug group).Suppose the severity of symptoms was substantially reduced for both the placebo and the treatment groups.What should be done next?

No matter what type of population value (or combination of population values) is being estimated using a confidence interval, what items should you be watching for, in order to best assess the results?

For Questions use the following narrative Narrative: Quiz times The introductory biology class at a large university is taught to hundreds of students each semester.For planning purposes, the instructor wants to find out the average amount of time that students would use to take the first quiz, if they could have as long as necessary to take it.She takes a random sample of 100 students from this population and finds that their average time for taking the quiz is 24 minutes, and the standard deviation is 16 minutes. -{Quiz times narrative} Find a 95% confidence interval for the average time to take this quiz for the whole population of students who take the class.

The formula for a confidence interval for the population mean is based on the rule for sample means, which has assumptions that need to be met.What are those assumptions? (Hint: there are different assumptions depending on whether or not the population is bell-shaped.)

For Questions , use the following narrative Narrative: Cell phone use How do men and women compare when it comes to talking on the cell phone? Suppose you take a random sample of 100 male cell phone owners and a random sample of 100 female cell phone owners.The average number of minutes for the women per month was 280 with a standard deviation of 10; the average number of minutes for the men per month was 190 with a standard deviation of 30. -{Cell phone use narrative} Based on these sample results, what is the difference in average time spent on the cell phone for females versus males?

For Questions , use the following narrative Narrative: Cell phone use How do men and women compare when it comes to talking on the cell phone? Suppose you take a random sample of 100 male cell phone owners and a random sample of 100 female cell phone owners.The average number of minutes for the women per month was 280 with a standard deviation of 10; the average number of minutes for the men per month was 190 with a standard deviation of 30. -{Cell phone use narrative} Suppose the women had only talked for 195 minutes per month, on average, and all the other statistics remained the same.Find the lower and upper limits for the resulting confidence interval (females - males), and interpret the results.Who's talking now?

The standard deviation of all possible sample means (from same sized samples) is called the _______________ of the mean.

Describe a general scenario where you would use a confidence interval for the difference between two means.

What three items are needed in order to construct a confidence interval to estimate the mean of a population?

For Questions , use the following narrative Narrative: Male weight loss Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13.4 and 18.3 pounds.These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. -{Male weight loss narrative} What is the sample mean?

What does it mean for a confidence interval for the difference of two means to contain zero?

How should you collect your data in order to use it in a confidence interval for the difference of two means?