Chapter 8: Confidence Interval Estimation
Multiple Choice


1.  

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

1.28
1.65
1.96
2.58


2.  

The z-value that is used to construct a 99% confidence interval is:

1.28
1.65
1.96
2.58


3.  

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

It is symmetric.
It's exact shape (i.e., spread) is characterized by the degrees of freedom.
As the sample size grows, it gradually approaches the normal distribution.
All of the above are properties of the t distribution.


4.  

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

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.
you can be 95% confident that you have selected a sample whose interval does include the population mean.
Both (a) and (b) are true.
Neither (a) nor (b) is Correct.


5.  

Which of the following statements is false?

There is a different z-value (i.e., critical value) used for each level of alpha.
It is possible to construct a 100% confidence interval estimate for the population mean.
Alpha is the proportion in the tails of the distribution which are outside of the confidence interval.
In practice, the population mean is an unknown quantity that is to be estimated.


6.  

The type of reasoning involved in obtaining confidence interval estimates is called:

deductive.
inductive.
a posteriori.
a priori.


7.  

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?

Your friend's interval has a greater degree of confidence.
Your interval has a greater degree of confidence.
Your interval is narrower.
Your interval is wider.


8.  

The value of alpha for a 98% confidence interval would be:

0.20
0.10
0.05
0.02


9.  

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

narrower for 99% confidence than for 95% confidence.
wider for a sample of size 100 than for a sample of size 50.
wider for 90% confidence than for 95% confidence.
wider when the sample proportion is 0.50 than when the sample proportion is 0.20.


10.  

When determining the sample size for a mean for a given level of confidence and standard deviation, if the sampling error (e) is allowed to increase, the sample size required:

will increase.
will decrease.
will stay the same.
cannot be determined.


11.  

The value of z selected for constructing a given confidence interval is called the ________ value.

critical
student
confidence
error


12.  

When estimating the population mean with a small sample, the t distribution may be used with ______ degrees of freedom.

n
n+1
n-1
n-2


13.  

A sample of 50 students was taken from the local university. These students spent an average of $170 on books this semester, with a standard deviation of $25.50. A 95% confidence interval for the average spent on books for all students would be ______.

170 plus or minus 3.462
170 plus or minus 5.95
170 plus or minus 8.42
None of these is correct.


14.  

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 ______.

2.921
2.898
2.853
2.567


15.  

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?

105
150
420
597


16.  

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

20
40
385
1537


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