Question 1

A sample of 36 coins has a mean weight of 1.01 pounds per box. The population standard deviation is 0.20. Construct an 80% confidence interval for the mean weight of all boxes. What is the correct formula for the margin of error in this scenario?

Accepted Answer

$$ME = Z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$$

Question 2

Given a sample mean of $$1.01$$, a population standard deviation of $$0.20$$, and a sample size of $$36$$, what is the 80% confidence interval for the population mean?

Accepted Answer

$$(0.956, 1.064)$$

Question 3

A car dealership wants to estimate the mean cost of its new model car with 80% confidence. The population standard deviation is $$2,517.8$$ and a sample of $$25$$ cars has a mean of $$96,520. $$What is the correct critical value ($$Z_{\alpha/2}) $$for an 80% confidence interval?

Accepted Answer

$$Z_{\alpha/2} = 1.28$$

Question 4

For the car dealership scenario, what is the 80% confidence interval for the mean cost of the new model car?

Accepted Answer

$$(93,700, 99,340)$$

Question 5

A random sample of size $$36 is $$selected from a normally distributed population with a mean of $$50$$ and a population standard deviation of $$6. $$What is the probability that the sample mean is between $$48.5$$ and $$51.0$$?

Accepted Answer

$$P(48.5 \u003c \bar{x} \u003c 51.0) = 0.7266$$

Question 6

Which formula is used to calculate the standard error of the mean when the population standard deviation is known?

Accepted Answer

$$SE = \frac{\sigma}{\sqrt{n}}$$

Question 7

If you want to be 95% confident that your sample mean is within $$0.5 of $$the population mean, and the population standard deviation is $$2.5$$, what sample size is required?

Accepted Answer

$$n = 97 ($$rounded up from 96.04)$

Question 8

Which of the following best describes a confidence interval?

Accepted Answer

A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter.

Question 9

In the context of confidence intervals, what does the confidence level represent?

Accepted Answer

The proportion of similarly constructed intervals that would contain the population parameter if the process were repeated many times.

Question 10

A company wants to study the average wage of mid-level managers. The standard deviation is $$5.25$$ per hour. What sample size is needed to be 95% confident that the estimate is within $$1.00 of $$the actual wage?

Accepted Answer

$$n = 96.04$$

Question 11

Which combination model would be the best based on the highest adjusted $$R^2$$ and significance?

Accepted Answer

Combination 4

Question 12

If the population standard deviation is unknown and the sample size is small ($$n \u003c 30$$), which distribution should be used to construct a confidence interval for the mean?

Accepted Answer

The $$t-$$distribution

Question 13

What is the effect of increasing the sample size on the width of a confidence interval, assuming all other factors remain constant?

Accepted Answer

The confidence interval becomes narrower.

Question 14

If the confidence level increases from 80% to 95%, what happens to the margin of error?

Accepted Answer

The margin of error increases.

Question 15

Which of the following is NOT an assumption for constructing a confidence interval for the mean when the population standard deviation is known?

Accepted Answer

The population standard deviation is unknown.

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