STAT412
Exam 1
PRACTICE QUESTIONS
Name___________________________
Multiple choice questions:
1. If we are performing a hypothesis test of H0: = 60 vs. Ha: > 60, the probability of rejecting H0 if 
will be ________ the probability of rejecting H0 if .
A) less than
B) greater than
C) equal to
D) not comparable to
2. Suppose a 95% confidence interval for  turns out to be (1,000, 2,100). Interpret the interval.
A) If many different samples (of the size used to construct the above interval) were selected and based on each
sample, a confidence interval were constructed, 95% of the time the value of  would lie between 1,000 and
2,100.
B) The method used to get the interval from 1,000 to 2,100, when used on infinitely many random samples of
the same size from the same population, produces intervals which include the population mean in 95% of the
intervals.
C) 95% of the observations in the entire population fall in the given interval.
D) 95% of the observations in the sample fall in the given interval.
3. Which one of the following examples involves independent samples.
A) For 15 randomly selected food items, the prices advertised in the local newspaper by two competing
supermarkets are recorded. A hypothesis test is then performed to see if there is any mean difference in the
prices offered by the two supermarkets.
B) A group of 50 students had their blood pressures measured before and after watching a movie containing
violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.
C) The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache
is cured for patients who use the medicine and another group of patients who use a placebo drug.
D) A study is conducted to compare the starting salaries of male and female college graduates who find jobs.
Pairs are formed by choosing a male and a female with the same-major and similar grade point averages.
Suppose a random sample of ten pairs is formed in this manner and the starting salary of each person is
conducted.
4. A researcher randomly selects 20 people from his state and records their cholesterol level. Using the sample
data, the following 95% confidence interval for the population mean cholesterol level was obtained: (218.54,
231.46). Based on this interval, which one of the null hypotheses below (versus a  research hypothesis) can be
rejected at =.05?
A) H0:  = 215
B) H0:  = 220
C) H0:  = 225
D) H0:  = 230
5. In the past, the mean running time for a certain type of flashlight battery has been 9.6 hours. The
manufacturer has introduced a change in the production method and wants to perform a significance test to
determine whether the mean running time has increased as a result. The hypotheses are:
H0: μ = 9.6 hours
Ha: μ > 9.6 hours
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a
Type I error, a Type II error, or a correct decision, if in fact the mean running time has increased.
A) Correct Decision
B) Type I Error
C) Type II error
D) Not enough information
6. A test of H0:  = 0 versus Ha: > 0 is conducted on the same population independently by two different
researchers. They both use the same sample size and the same value of  = 0.05. Which of the following will
have to be the same for both researchers?
A) The p-value of the test.
B) The power of the test if  = 6.
C) The value of the test statistic.
D) The decision about whether or not to reject the null hypothesis.
7. A random sample of 500 female students will be selected and their heights will be measured.
The quantities x 
A)
B)
C)
D)
s
will then be calculated. The result will be a
n
95% confidence interval.
90% confidence interval.
84% confidence interval.
68% confidence interval.
8. A student performs a hypothesis test to test a claim regarding a population mean. The population is normally
distributed, the population standard deviation is unknown, and the sample size is less than 30. The significance
level is supposed to be 0.05. However, the student incorrectly uses the standard normal distribution instead of
the t-distribution. Will the actual significance level of the test be greater than 0.05, less than 0.05, or will it still
be equal to 0.05?
A) Greater than .05
B) Less than .05
C) Equal to .05
D) Not enough information to decide
9. Scores of adults on the Wechsler Adult Intelligence Scale (a common "IQ" test) follow a normal distribution.
The middle 95% of scores on this test range from 70 to 130. What is the standard deviation of the test scores?
A)
B)
C)
D)
20 points
15 points
10 points
7.5 points
10. What is the primary purpose of a confidence interval for a mean?
A) to estimate a sample mean
B) to test a hypothesis about a sample mean
C) to estimate a population mean
D) to provide an interval that covers 95% of the individual values in the population
11. Which of the following statements are true?
A) When the research hypothesis is H a :   o , the null hypothesis H o should be rejected if x is too far to the
right of o .
B) When the research hypothesis is H a :   o , the null hypothesis H o should be rejected if x is too far to the
left of o .
C) When the research hypothesis is H a :   o , the null hypothesis H o should be rejected if x is too far to
either side of o .
D) All are true.
12. The primary purpose of a hypothesis test is to
A) estimate the p-value of a sample
B) estimate the p-value of a population.
C) decide whether there is enough evidence to support a research hypothesis about a sample.
D) decide whether there is enough evidence to support a research hypothesis about a population.
Problems: Make sure you show all of your work for the problems!
13. Ten different families are tested for the number of gallons of water a day they use before and after viewing a
conservation video. Using the relevant output below, conduct hypothesis test using =.05.
N
Mean StDev
Before
10 35.80
3.43
After
10 31.00
3.53
Difference 10
4.80
5.25
H0: _____________
Ha: _____________

=.05
Specify rejection region:
Calculate test statistic:
State your conclusion:
Approximate the p-value:
14. Scores on a national writing exam are approximately normally distributed, with a mean of 490 and a
standard deviation of 20. Consider random samples of size 16 from the population of test takers.
a) Sketch the sampling distribution of the sample mean. You need not get the graph perfectly correct, but should
clearly indicate different aspects of the distribution, such as mean, standard deviation, and shape.
b) Find the probability that a random sample of 16 test takers will have a mean exam score that is greater than
498?
c) Find k such that P( x < k) = .025.
15. Black bears (Ursus americanus) have a tendency to wander for food, and they have a high level of
curiosity. These characteristics will sometimes get them into trouble when they travel through human-use
areas such as parks. When they become "nuisances," the Park Service transplants them if possible to other
areas. The outcomes of such transplants in Glacier National Park over a 10-year period are given in the table
below:
Transplanted Bear Table
Successful
Returned to capture area
Nuisance in another area
Killed outside of park
Totals
Male
32
34
14
3
83
Female
17
45
4
4
70
Totals
49
79
18
7
153
a) From these data, estimate the probability that a randomly selected transplanted bear would be female
or nuisance in another area.
b) After combining the above data with other National Parks, officials estimated that only about 18% of
black bears in all parks become enough of a nuisance to be transplanted. They further estimate that
80% of nuisance bears are male, and 55% percent of non-nuisance bears are females. If a randomly
selected bear is observed to be a male, what is the probability it will be a nuisance?
16. How much sugar do reduced sugar cookies typically have? You take a random sample of 21 reduced-sugar
cookies and test them in a lab, finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams
of sugar. Create a 95% confidence interval for the mean grams of sugar.
17. Consider a test of Ho:  = 65 versus Ha:  < 65. The test uses  = 10, =.05 and a sample size of n = 100.
a. Describe the sampling distribution of x assuming Ho is true.
Mean=
Standard deviation=
Shape:
Sketch the sampling distribution.
b. Describe the sampling distribution of x if = 63.
Mean=
Standard deviation=
Shape:
On your graph of part a, sketch the sampling distribution of x if = 63.
c. Find the probability of failing to reject H0 if  is actually equal to 63, that is find the probability of
making a Type 2 error. Shade the area corresponding to this probability on your graph.