Confidence Intervals

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Questions and Answers

What does a point estimate indicate about a population parameter?

It provides the exact value of the population mean.
It confirms that prior data is irrelevant to the population mean.
It serves as an approximation of the population mean. (correct)
It reflects the uncertainty associated with the estimate.

Why are confidence intervals considered more informative than point estimates?

They provide a range where the true mean is likely to fall. (correct)
They require weighing all population members before calculations.
They eliminate any uncertainty regarding the population mean.
They are easier to calculate than point estimates.

What is the proper interpretation of a 95% confidence interval?

95% of all possible confidence intervals will contain the population mean. (correct)
The sample mean must be exactly equal to the population mean.
There is a 95% chance the population mean is within the interval.
Confidence intervals are fixed and do not vary across samples.

How does prior information about sample means influence confidence intervals?

It can invalidate the confidence interval's relevance. (C) Signup and view all the answers

What does the notation 72.85 < μ < 107.15 represent in a confidence interval?

It delineates a range for the population mean with 95% confidence. (D) Signup and view all the answers

What is the consequence if a confidence interval does not account for prior studies indicating higher means?

The confidence interval could be misleading. (D) Signup and view all the answers

Which of the following defines the purpose of a confidence interval?

To indicate a range where the population mean is likely found. (D) Signup and view all the answers

What percentage of confidence intervals is expected to NOT contain the population mean at a 95% confidence level?

5% (C) Signup and view all the answers

What is a potential limitation of relying solely on confidence intervals?

They may not represent the population well if no prior data is considered. (D) Signup and view all the answers

Which scenario suggests that a 95% confidence interval may not be reliable?

When previous studies indicate a mean above the upper interval limit. (A) Signup and view all the answers

What is one key characteristic of the standard method of computing confidence intervals?

Each interval is contiguous. (B) Signup and view all the answers

How is the standard error of the mean calculated if the population standard deviation is known?

It is the population standard deviation divided by the square root of the sample size. (B) Signup and view all the answers

What conditions warrant the use of the t distribution instead of the normal distribution?

When the sample size is small and the population variance is estimated. (B) Signup and view all the answers

What is the formula used to compute a 95% confidence interval for the mean?

Lower limit = M - Z.95 * σM; Upper limit = M + Z.95 * σM. (D) Signup and view all the answers

What value of Z is typically used to determine the limits of a 95% confidence interval in a normal distribution?

1.96 (A) Signup and view all the answers

What does the term 'leptokurtic' describe in relation to the t distribution?

It has a shape that is more peaked than the normal distribution. (D) Signup and view all the answers

When using the normal distribution with a sample size of 100 or above, what can be said about the t distribution?

It becomes similar to the standard normal distribution. (D) Signup and view all the answers

What must be true in order to compute a confidence interval for a population mean?

Sample data must be normally distributed. (C) Signup and view all the answers

If a researcher intends to calculate a 99% confidence interval, what is the corresponding value of Z used?

2.58 (B) Signup and view all the answers

What is the lower limit of the 95% confidence interval for the mean difference score?

14.17 (C) Signup and view all the answers

What is the critical value of t used in the computation for the 95% confidence interval for this data?

2.013 (D) Signup and view all the answers

What does the standard error of the mean represent in this context?

The measure of variability in the sample mean estimate. (B) Signup and view all the answers

What is the upper limit of the 95% confidence interval for the mean difference score?

18.56 (A) Signup and view all the answers

If the sample mean (M) is 16.362, what does the term 'sM' refer to in the 95% confidence interval formula?

The estimated standard error of the mean. (B) Signup and view all the answers

In the analysis of the Stroop data, how many subjects were recorded for the color-naming task?

47 (B) Signup and view all the answers

What is the calculated standard deviation of the mean time difference for the 47 subjects?

7.470 (B) Signup and view all the answers

How is the term 'interference effect' defined in the context of this analysis?

The effect of naming ink colors that conflict with the written word. (A) Signup and view all the answers

What is the formula used to compute the confidence interval?

Lower limit = M - (tCL)(sM); Upper limit = M + (tCL)(sM) (B) Signup and view all the answers

In the given example, what was the mean time difference for all subjects?

16.362 seconds (C) Signup and view all the answers

Study Notes

Point Estimates

A point estimate is a single value used to estimate a population parameter
It doesn't reveal the uncertainty associated with the estimate