Question 1

Which of the following best describes a point estimate for the population mean $$\mu$$?

Accepted Answer

A single value calculated from the sample data that serves as the best unbiased estimate of the population mean.

Question 2

A researcher collects a random sample of 40 student-athletes and finds their mean weekly hours spent on required athletic activities is 19.6. What is the point estimate for the population mean?

Accepted Answer

19.6

Question 3

Which formula is used to calculate the margin of error $$E$$ for a confidence interval for the mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$E = z_c \frac{\sigma}{\sqrt{n}}$$

Question 4

If a 95% confidence interval for the mean number of hours spent per week on required athletic activities is (19.2, 20.0), what does this mean?

Accepted Answer

If many samples are taken, about 95% of the intervals constructed will contain the true population mean.

Question 5

A college admissions director wants to estimate the mean age of all students. In a random sample of 20 students, the mean age is 22.9 years, the population standard deviation is 1.5 years, and the population is normally distributed. What is the correct formula to construct a 90% confidence interval for the population mean?

Accepted Answer

$$\bar{x} \pm z_c \frac{\sigma}{\sqrt{n}}$$

Question 6

Which of the following statements about the level of confidence is correct?

Accepted Answer

It is the probability that the interval estimation process will produce intervals containing the population parameter in repeated sampling.

Question 7

A researcher wants to be 95% confident that the sample mean is within 0.5 hour of the population mean. The population standard deviation is 1.2 hours. What is the minimum sample size required?

Accepted Answer

$$n = \left( \frac{z_c \sigma}{E} \$$right)^2$$

Question 8

Which of the following is a correct interpretation of a 99% confidence interval for a population mean?

Accepted Answer

If the sampling process is repeated many times, about 99% of the constructed intervals will contain the population mean.

Question 9

Which of the following is NOT an assumption for constructing a confidence interval for the mean when $$\sigma is $$known?

Accepted Answer

The population standard deviation is unknown.

Question 10

A sample of 50 patients has a mean cholesterol level of 200 mg/dL. The population standard deviation is known to be 20 mg/dL. What is the 95% confidence interval for the population mean cholesterol level? (Use $$z_c = 1.96)$$

Accepted Answer

($$194.47$$, $$205.53)$$

Question 11

Which of the following best describes the margin of error in a confidence interval?

Accepted Answer

The greatest possible distance between the point estimate and the value of the parameter it is estimating.

Question 12

If the sample size increases while keeping the confidence level the same, what happens to the margin of error?

Accepted Answer

It decreases.

Question 13

A 90% confidence interval for the mean age of students is (22.3, 23.5). Which of the following is an incorrect interpretation?

Accepted Answer

There is a 90% probability that the actual mean is in the interval (22.3, 23.5).

Question 14

Which of the following is the correct formula for a confidence interval for the population mean when $$\sigma is $$known?

Accepted Answer

$$\bar{x} \pm z_c \frac{\sigma}{\sqrt{n}}$$

Question 15

A researcher wants to estimate the mean number of hours spent per week on required athletic activities by all student-athletes. The population standard deviation is 1.2 hours, and the researcher wants to be 95% confident that the sample mean is within 0.4 hour of the population mean. What is the minimum sample size required? (Use $$z_c = 1.96)$$

Accepted Answer

35

Confidence Intervals for the Mean (σ Known)

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