Question 1

What is the formula for the confidence interval of the population mean when the population variance is known?

Accepted Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Question 2

What is the formula for the confidence interval of the population mean when the population variance is unknown?

Accepted Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Question 3

In constructing a confidence interval for the population mean, if the confidence level increases, what happens to the width of the confidence interval?

Accepted Answer

Increases

Answer

Stays the same

Answer

Decreases

Answer

Depends on the sample size

Question 4

A researcher wants to estimate the average height of students in a university with 95% confidence. If the population standard deviation is 4 inches and the sample size is 100, what is the margin of error?

Accepted Answer

0.78 inch

Answer

0.64 inch

Answer

0.96 inch

Answer

1.28 inch

Question 5

A random sample of 50 observations is drawn from a normally distributed population. The sample mean is 75 and the population standard deviation is 10. What is the 90% confidence interval for the population mean?

Accepted Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Answer

$\overline{\mathrm{x}}\ \pm\ Z\ \frac{\delta}{\sqrt{n}}$

Question 6

In constructing a confidence interval for the population mean with unknown variance, which distribution is used to determine the critical value?

Accepted Answer

T-distribution

Answer

Chi-square distribution

Answer

Normal distribution

Answer

F-distribution

Question 7

A researcher wants to estimate the average weight of newborn babies in a hospital with 95% confidence. If a sample of 25 newborns has a sample mean weight of 7 pounds and a sample standard deviation of 1.5 pounds, what is the margin of error?

Accepted Answer

0.62 pounds

Answer

0.97 pounds

Answer

0.51 pounds

Answer

0.78 pounds

Question 8

A random sample of 27 observations is drawn from a population with an unknown variance. The sample mean is 50, and the sample standard deviation is 8. What is the 95% confidence interval for the population mean?

Accepted Answer

50±2.056× $\frac{8}{\sqrt{27}}$

Answer

50±1.96× $\frac{8}{\sqrt{27}}$

Answer

50 ± 2.056

Answer

50 ± 1.96

Question 9

A researcher wants to estimate the average time spent daily on social media by teenagers with 90% confidence. If a sample of 25 teenagers shows a mean time of 2.5 hours and a sample standard deviation of 0.5 hours, what is the margin of error?

Accepted Answer

0.171 hour

Answer

0.312 hour

Answer

0.156 hour

Answer

0.624 hour

Question 10

A random number of n = 24 data from a normal distribution with unknown variance produced and $\frac{8}{\sqrt{27}}$ = 42.5 and s = 2.6. What is the lower limit of the 90% confidence intervalfor the population mean?

Accepted Answer

41.59

Answer

43.60

Answer

40.40

Answer

30.32

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