Question 1

Which of the following best describes a point estimate in statistics?

Accepted Answer

A single statistic determined from a sample used to estimate the corresponding population parameter.

Question 2

A university wants to estimate the mean hours worked by students. If the population standard deviation is known to be 5 hours, and a random sample of 64 students has a mean of 23 hours, what is the 90% confidence interval for the mean hours worked? (Use $$z = 1.645$$ for 90% confidence)

Accepted Answer

$$23 \pm 1.03$$ hours, so the interval is $$[21.97, 24.03]$$

Question 3

Which statement about confidence intervals is TRUE?

Accepted Answer

The margin of error is half the width of the confidence interval estimate.

Question 4

A company wants to estimate the proportion of customers who will redeem a coupon. In a sample of 100, 22 redeemed it. What is the 99% confidence interval for the population proportion? (Use $$z = 2.576$$ for 99% confidence)

Accepted Answer

$$[0.1133, 0.3267]$$

Question 5

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

Accepted Answer

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

Question 6

When estimating a population mean and the population standard deviation is unknown, which distribution should be used?

Accepted Answer

t-distribution

Question 7

A random sample of 10 employees at a manufacturing company has a mean overtime of 4.5 hours and a sample standard deviation of 1.3 hours. What is the 95% confidence interval for the population mean overtime? (Use $$t = 2.262$$ for 9 degrees of freedom)

Accepted Answer

$$[3.57, 5.43]$$ hours

Question 8

Which of the following factors does NOT increase the required sample size for a confidence interval?

Accepted Answer

Lower population variation

Question 9

A political advisor wants to estimate the proportion of voters for a candidate with a 90% confidence interval and a margin of error of 0.05. Without a pilot sample, what value should be used for $$p to $$conservatively estimate the required sample size?

Accepted Answer

$$p = 0.5$$

Question 10

Which formula is used to estimate the standard error of the sample proportion?

Accepted Answer

$$\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$

Question 11

If a sample size is increased while keeping the confidence level constant, what happens to the margin of error?

Accepted Answer

It decreases.

Question 12

A marketing firm wants a 95% confidence interval for the proportion of customers with a favorable response, with a margin of error of 0.05. In a pilot sample of 40, 33 responded favorably. How many additional people should be surveyed?

Accepted Answer

At least 385 more people

Question 13

Which of the following is TRUE about the t-distribution compared to the standard normal distribution?

Accepted Answer

The t-distribution is more spread out than the standard normal distribution.

Question 14

A sample of 8 crashed cars has a mean damage of $$7,250 and a sample standard deviation of 1$$,133. What is the 90% confidence interval for the population mean damage? (Use $$t = 1.860$$ for 7 degrees of freedom)

Accepted Answer

$$[6,505.13, 7,994.87]$$

Question 15

Which formula is used to determine the required sample size for estimating a population mean with a known standard deviation?

Accepted Answer

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

Question 16

Which of the following is NOT a conflicting objective when determining sample size for a confidence interval?

Accepted Answer

Large margin of error

Question 17

If the population standard deviation is unknown, which formula should be used for the confidence interval estimate for the mean?

Accepted Answer

$$\bar{x} \pm t \frac{s}{\sqrt{n}}$$

Question 18

Which of the following best describes the relationship between confidence level and margin of error?

Accepted Answer

Increasing the confidence level increases the margin of error.

Question 19

A sample mean is $$2,000$$ with a population standard deviation of $$400$$ and sample size $$n = 100. $$What is the margin of error for a 95% confidence interval? (Use $$z = 1.96)$$

Accepted Answer

$$78.40$$

Estimating Single Population Parameters: Confidence Intervals and Sample Size

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