Q: If you are given the lower and upper limits of a confidence interval, how do you calculate the sample mean $$\bar{x}$$?

$$\bar{x} = \dfrac{\text{upper limit} + \text{lower limit}}{2}$$

Question 1

Which of the following statements about the Student t distribution is TRUE?

Accepted Answer

As the sample size increases, the Student t distribution approaches the standard normal distribution.

Question 2

A researcher wants to estimate the mean weight of a population but does not know the population standard deviation. Which distribution should be used to construct a confidence interval for the mean?

Accepted Answer

Student t distribution

Question 3

Given a sample mean $$\bar{x} = 88.75$$, a sample size $$n = 36$$, and a 95% confidence interval of (85.74, 91.76), what is the margin of error $$E$$?

Accepted Answer

$$E = 3.01$$

Question 4

Which of the following is a requirement for constructing a confidence interval for a population mean $$\mu$$ when $$\sigma is $$unknown?

Accepted Answer

The sample must be a simple random sample.

Question 5

If a 98% confidence interval for the mean change in LDL cholesterol after a garlic treatment includes 0, what does this suggest?

Accepted Answer

The garlic treatment has no significant effect on LDL cholesterol.

Question 6

What is the formula for the margin of error $$E$$ when constructing a confidence interval for the mean with unknown $$\sigma$$?

Accepted Answer

$$E = t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}$$

Question 7

A 99% confidence interval for the mean weight of Hershey Kisses is (4.4688 g, 4.5732 g). What is the best point estimate for the population mean?

Accepted Answer

$$4.5210 g$$

Question 8

Which of the following best describes the degrees of freedom for a t-distribution when estimating a population mean?

Accepted Answer

$$df = n - 1$$

Question 9

Suppose you want to estimate the mean pulse rate of adult males with 99% confidence and a margin of error of 2 bpm. If the sample standard deviation is $$s = 11.3$$ bpm, what formula should you use to determine the minimum sample size $$n$$?

Accepted Answer

$$n = \left[ \dfrac{z_{\alpha/2} \cdot \sigma}{E} \right]^2$$

Question 10

If the range of pulse rates in a sample is 64 bpm, what is the estimated standard deviation using the range rule of thumb?

Accepted Answer

$$\sigma \approx 16$$ bpm

Question 11

A 90% confidence interval for the mean arsenic content in California brown rice is calculated. Can this interval be used to describe arsenic levels in Arkansas brown rice?

Accepted Answer

No, because the samples are from different populations.

Question 12

Which of the following is the correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 13

Which of the following is NOT a property of the Student t distribution?

Accepted Answer

Its standard deviation is always equal to 1.

Question 14

If you are given the lower and upper limits of a confidence interval, how do you calculate the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \dfrac{	ext{upper limit} + 	ext{lower limit}}{2}$$

Question 15

A sample of size $$n = 10 is $$drawn from a normal population with unknown mean and standard deviation. Which distribution should be used to construct a 95% confidence interval for the mean?

Accepted Answer

Student t distribution with 9 degrees of freedom

Estimating Parameters and Determining Sample Sizes: Confidence Intervals for the Population Mean

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