1.
A basketball player makes 160 out of 200 free throws. We would estimate the probability that the player makes his next free throw to be
A.
0.16.
B.
50−50. Either he makes it or he doesn't.
C.
0.80.
D.
1.2.


You select an employee at random from all those in a large company. An employee can be either male or female, and can be under 30 years old, between 30 and 45 years old, or over 45 years old. The table below gives the probability of each of the six possible age and gender combinations for a randomly selected employee.
 
 
Under 30
30 – 45
Over 45
Under 30
30 – 45
Over 45
Age – gender combination
Male
Male
Male
Female
Female
Female
Probability
.3
.3
?
.1
.1
.1
 


2.
The probability that the employee selected is a male over 45 is
A.
.1.
B.
.2.
C.
.3.
D.
impossible to determine from the information given.


You select an employee at random from all those in a large company. An employee can be either male or female, and can be under 30 years old, between 30 and 45 years old, or over 45 years old. The table below gives the probability of each of the six possible age and gender combinations for a randomly selected employee.
 
 
Under 30
30 – 45
Over 45
Under 30
30 – 45
Over 45
Age – gender combination
Male
Male
Male
Female
Female
Female
Probability
.3
.3
?
.1
.1
.1
 


3.
The probability that I select neither a male nor a female under 30 years of age is
A.
.1.
B.
.3.
C.
.4.
D.
.6.


4.
A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and standard deviation 10. The average of the observations in our sample is to be computed. The sampling distribution of is
A.
normal with mean 60 and standard deviation 10.
B.
normal with mean 60 and standard deviation 2.
C.
normal with mean 60 and standard deviation 0.4.
D.
normal with mean 12 and standard deviation 2.


5.
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores, what is the mean of the sampling distribution of the average (sample mean) score for the 36 students?
A.
1.0
B.
3.1
C.
6.0
D.
18.6


6.
I take an SRS of size n from a population that has mean 80 and standard deviation 20. How big should n be so that the sampling distribution of has standard deviation 1?
A.
400
B.
20
C.
Approximately 5
D.
Cannot be determined unless we know the population follows a normal distribution.


7.
A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 9 ± 3. We may conclude
A.
there is a 95% probability that μ is between 6 and 12.
B.
there is a 95% probability that the true mean is 9 and there is a 95% chance that the true margin of error is 3.
C.
if we took many, many additional random samples and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ.
D.
all of the above.


8.
You measure the weights of a random sample of 400 male workers in the automotive industry. The sample mean is = 176.2 lbs. Suppose that the weights of male workers in the automotive industry follow a normal distribution with unknown mean μ and standard deviation σ = 11.1 lbs. A 95% confidence interval for μ is
A.
(154.44, 197.96).
B.
(157.94, 194.46).
C.
(175.11, 177.29).
D.
(175.29, 177.11).


9.
A small New England college has a total of 400 students. The Math SAT score is required for admission and the mean score of all 400 students is 620. The population standard deviation is found to be 60. The formula for a 95% confidence interval yields the interval 640 ± 5.88. We may conclude
A.
the interval is incorrect. It is much too small.
B.
if we repeated this procedure many, many times, only 5% of the 95% confidence intervals would fail to include the mean Math SAT score of the population of all students at the college.
C.
95% of the time, the population mean will be between 634.12 and 645.88.
D.
none of the above.


10.
An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The mean lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically significant at the 0.05 level. If, in fact, there is no difference between the mean lifetimes of the new and old designs, the researcher has
A.
committed a type I error.
B.
committed a type II error.
C.
a probability of being correct, which is equal to the P-value.
D.
a probability of being correct, which is equal to 1 – (P-value).


11.
Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a random sample of nine employees of your company (that you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. It takes them an average of = 31.2 seconds to complete the maze. Use this information to test the hypotheses

H0: μ = 30, Ha: μ ≠ 30

at the 1% significance level You conclude
A.
that H0 should be rejected.
B.
that H0 should not be rejected.
C.
that Ha should be accepted.
D.
this is a borderline case and no decision should be made.


12.
An agricultural researcher plants 25 plots with a new variety of corn that is drought resistant and hence potentially more profitable. The average yield for these plots is = 150 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean μ and that a 95% confidence interval for μ is found to be 150 ± 3.29. Which of the following is true?
A.
A test of the hypotheses H0: μ = 150, Ha: μ ≠ 150 would be rejected at the 0.05 level.
B.
A test of the hypotheses H0: μ = 150, Ha: μ > 150 would be rejected at the 0.05 level.
C.
A test of the hypotheses H0: μ = 160, Ha: μ ≠ 160 would be rejected at the 0.05 level.
D.
All the above.


A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest.


13.
The probability that the researcher will commit a type I error is
A.
0.01.
B.
0.10.
C.
0.90.
D.
equal to the P-value and cannot be determined until the data have been collected.


14.
Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a random sample of nine employees of your company (who you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. You compute the average of their times to complete the maze and will use this information to test the hypotheses

H0: μ = 30, Ha: μ ≠ 30.

at the 1% significance level. The power of your test at μ = 28 seconds is approximately
A.
less than 0.001.
B.
0.0630.
C.
0.2810.
D.
0.4877.


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