Question 1

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.

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Question 2

Suppose you are comparing the proportion of people who successfully stopped smoking on each of two different smoking cessation plans.You randomly assigned subjects to treatment, but you also collected data on each subject on a variety of measurement variables as well.How can this help you to verify that your randomization procedure worked?

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Question 3

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} Does there appear to be a difference in the relative risks of having bad side effects for the new drug, compared to the standard drug? Use confidence intervals to give you a general idea.

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Question 4

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?

Accepted Answer

The confidence interval includes both negative and positive values, indicating uncertainty about the direction of the difference in means (A). The interval's range does not imply certainty about which species weighs more, only that there is a range of plausible values for the difference in means (B). A narrower confidence interval (like 90%) might exclude zero, suggesting a significant difference, but this depends on the actual calculation and is not guaranteed by the information given (C).

Question 5

Which of the following factors can make it difficult to make correct conclusions about the population based on confidence intervals?

Accepted Answer

All of the above factors can make it difficult to make correct conclusions about the population. Bias in data collection or sampling process can lead to inaccurate representation of the population. Confounding variables can lead to incorrect associations between variables. Small sample sizes can lead to a lack of statistical power to detect true differences in the population.

Question 6

To get the standard error for the difference in the means of two independent samples, you take the square root of the __________ of the squares of the individual standard errors.

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Question 7

The difference in the means of two independent samples has __________ variability than the mean of the differences in a matched-pairs sample.(Assume sample sizes are comparable and the values in the pairs are positively correlated.)

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The answer of The difference in the means of two...

Question 8

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

Accepted Answer

When a confidence interval for the difference of two means contains zero, it implies that there is a possibility that there is no difference between the population means (A), that different samples could yield intervals that are above, below, or contain zero (B), and that the interval itself will have both negative and positive numbers, indicating uncertainty about the direction of the difference (C). Thus, all the given options are correct interpretations.

Question 9

Journal articles often report means and standard deviations, and they also often report their results in the form (mean +/− standard deviation).Does this latter form represent a real confidence interval for the population mean? If yes, explain why.If not, tell what it does represent.(Assume the populations are bell-shaped.)

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The answer of Journal articles often report means and standard...

Question 10

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?

Accepted Answer

All three items listed (A, B, and C) are important factors to consider when assessing the results of a confidence interval. It is important to ensure that the sample(s) selected are representative of the population(s) being studied, so that the results can be generalized with confidence. The confidence level should also be clearly stated, so that readers understand the level of certainty (or uncertainty) in the results. Finally, it is important to understand the type of study design used to generate the data, as this can affect the validity of any causal claims made by the researchers.

Question 11

Are all confidence intervals (whether they be for population means, proportions, or anything else) symmetric around their respective sample values? Explain.

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Question 12

For a 95% confidence interval, the value of 95% is called the _______________.

Accepted Answer

The answer of For a 95% confidence interval, the value...

Question 13

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?

Accepted Answer

Since the severity of symptoms was reduced for both the placebo and drug groups, it is important to take into account the placebo effect in order to determine if the drug treatment provides any additional benefit. Therefore, comparing the two groups directly will allow us to examine the specific influence of the drug treatment on the reduction of symptoms. Ignoring the placebo group or concluding that the drug doesn't do any better job than the placebo does would both be premature and incorrect conclusions without directly comparing the two groups.

Question 14

Suppose you want to calculate a confidence interval to estimate the population mean.What happens if you want to be more than 95% confident in your results but you can't take another sample? (Assume data quality is not an issue.)

Accepted Answer

To achieve a confidence level higher than 95%, you need to increase the confidence level (A), which requires using a larger multiplier (typically derived from the z-score or t-score) than 2 (B). This results in a wider confidence interval (C) because the margin of error increases with the larger multiplier.

Question 15

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 two things: the means and the __________.

Accepted Answer

The answer of You can determine confidence intervals for individual...

Question 16

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} How would you have interpreted the results if either of these two confidence intervals had contained the value 1.0?

Accepted Answer

The answer of For Questions , use the following narrative
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Question 17

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 __________.

Accepted Answer

The answer of You can determine confidence intervals for individual...

Question 18

If a researchers in an observational study attempts to control for a confounding variable, is it more likely that the resulting confidence interval will be wider or narrower than the confidence interval when he/she didn't control for the confounding variable?

Accepted Answer

Controlling for a confounding variable reduces bias and makes the confidence interval more precise, resulting in a narrower confidence interval.

Question 19

A confidence level is a measure of how much confidence we have that the __________ we used to generate the interval worked.

Accepted Answer

The answer of A confidence level is a measure of...

Question 20

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} Explain, in words a non-statistics student would understand, what the first confidence interval in this example means.

Accepted Answer

The answer of For Questions , use the following narrative
Narrative:...

Quiz 21: The Role of Confidence Intervals in Research

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 factors can make it difficult to make correct conclusions about the population based on confidence intervals?

To get the standard error for the difference in the means of two independent samples, you take the square root of the __________ of the squares of the individual standard errors.

The difference in the means of two independent samples has __________ variability than the mean of the differences in a matched-pairs sample.(Assume sample sizes are comparable and the values in the pairs are positively correlated.)

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

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?

Are all confidence intervals (whether they be for population means, proportions, or anything else) symmetric around their respective sample values? Explain.

For a 95% confidence interval, the value of 95% is called the _______________.

Suppose you want to calculate a confidence interval to estimate the population mean.What happens if you want to be more than 95% confident in your results but you can't take another sample? (Assume data quality is not an issue.)

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 two things: the means and the __________.

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 __________.

If a researchers in an observational study attempts to control for a confounding variable, is it more likely that the resulting confidence interval will be wider or narrower than the confidence interval when he/she didn't control for the confounding variable?

A confidence level is a measure of how much confidence we have that the __________ we used to generate the interval worked.