2. QUESTION

CONSIDER THE FOLLOWING MULTIPLE-CHOICE QUESTIONS

CIRCLE YOUR SELECTION CLEARLY:

What is the best description of a point estimate?

a. Any value from the sample used to estimate a parameter

b. A sample statistic used to estimate a parameter

c. The margin of error used to estimate a parameter.

[1]

Which best describes the lower endpoint of a confidence interval?

a. point estimate

b. point estimate minus margin of error

c. point estimate minus standard error

[1]

Which one of the following random variables would require that the confidence interval for the proportion, rather than the mean, be used?

a. the volume in ml of bottle fill-weight

b. the number of employees who vote "in favour," rather than "against," a new over-time policy

c. the number of sales per employee in 2021

d. the weight in kilograms of bags of fertilizer

[1]

Each of the following factors must be known in order to determine the sample size for quantitative (numerical) data, except for

a. the desired confidence level

b. the acceptable sampling error

c. the population standard deviation

d. the sample standard deviation

A confidence interval estimate is constructed around

a. the degree of confidence

b. the population parameter

c. the population mean

d. the point estimate

The z-value that is used to construct a 95% confidence interval is:

a. 2.58

b. 1.65

c. 1.96

d. 1.28

Which of the following is NOT a property of the student's t distribution?

a. It's exact shape (i.e., spread) is characterized by the degrees of freedom

b. It is symmetric

c. All of the above are properties of the t distribution

d. As the sample size grows, it gradually approaches the normal distribution

A 95% confidence interval for the mean can be interpreted to mean that:

a. you can be 95% confident that you have selected a sample whose interval does not include the population mean

b. if all possible populations are taken and confidence intervals are calculated, 95% of those intervals would include the true sample mean somewhere in their interval

c. if all possible samples are taken and confidence intervals are calculated, 95% of those intervals would include the true sample mean somewhere in their interval

d. if all possible samples are taken and confidence intervals are calculated, 95% of those intervals would include the true population mean somewhere in their interval

Which of the following statements is false?

a. Alpha is the proportion in the tails of the distribution which are outside of the confidence interval

b. In practice, the population mean is an unknown quantity that is to be estimated

c. There is a different z-value (i.e., critical value) used for each level of alpha

d. It is possible to construct a 100% confidence interval estimate for the population mean

You and your friend decide to construct 95% confidence intervals for a given population mean. You wind up taking a sample of 49 random observations while your friend's sample is made up of 36 random observations. Which of the following is true?

a. The total width of your confidence interval estimate is wider

b. Your friend's interval has a greater degree of confidence

c. The total width of your confidence interval estimate is narrower

d. Your interval has a greater degree of confidence

Calculations:

The width of a confidence interval for a proportion will be:

a. wider for a sample of size 100 than for a sample of size 50

b. wider for 90% confidence than for 95% confidence

c. narrower for 99% confidence than for 95% confidence

d. wider when the sample proportion is 0.50 than when the sample proportion is 0.20

Calculations:

A sample of 50 students was taken from the local university. These students spent an average of R170 on books this semester, with a standard deviation of R25.50. A 95% confidence interval for the average spent on books for all students would be ______.

a. None of these is Correct

b. 170 plus or minus 5.95

c. 170 plus or minus 3.462

d. 170 plus or minus 8.42

Calculations:

The t-value that would be used to construct a 99% confidence interval for the mean with a sample of size n=17 would be ______

a. 2.898

b. 2.567

c. 2.921

d. 2.583

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?

a. 420

b. 150

c. 105

d. 597