Download 9:30 Exam 2 - Spring, 2008 with answers

1. Assuming all requirements are met when calculating a 95% confidence interval for the population
average, you are 100% sure
a. the wind is from the north
b. the average of all possible sample means is the population mean
c. statistics is not important (you had better NOT choose this answer)
d. statistics will give you the correct value of the population mean
e. the confidence interval is incorrect
2. The power of a test can be written as
a.

c.
d.
e.
3. If you wish to support that the average temperature of men is above 98.6, then the rejection region
would be
a. all the answers are correct
b. two-sided
c. left-sided
d. right-sided
e. the null hypothesis
4. The grades on a test are normally distributed with a mean of 75 and a standard deviation of 10. You
have a grade of 80. What percent of the students made grades higher than yours?
a. none of the others are correct.
b. 0.50%
c. 0.05%
d. 30.85%
e. depends on how many people will take the class next year
5. What would be the conclusion of a confidence interval for the mean number of pages in science fiction
books, if the sample mean is 400, the typical error of the sample mean is 20 and the sample size is 100?
Assuming the population standard deviation is known, we are 95% confident that …
a. the sample average number of books is 400 with a margin of error of 2.
b. the population mean is 400
c. the average number of pages in all books falls between 360.8 and 439.2
d. the typical error is 2
e. I do not like this problem. (I am 100% sure you should not choose this one)
6. If the null hypothesis is “You should not be audited by the IRS” but based on your tax return, the IRS
believes you should be audited, then their conclusion is a(n)
a. type I error
b. beta
c. null hypothesis
d. type II error
e. no error has resulted
7. If the sample mean is 10, the population standard deviation is 20, and the sample size is 25, then the
standard error is
a. none of the others are correct
b. 20
c. 
d. 2
e. 4
8. You are sampling from a normal distribution with sigma known. What p-value corresponds to a test
statistic value of 2.33? (H1  > 20)
a. none of the other answers are correct.
b. 0.025
c. 0.99.
d. 0.02.
e. Can not be solved. More information is needed..
9. A sample proportion is a special case of
a. nothing
b. a sample mean
c. a non random sample
d. a rejection region
e. a variance
10. 0.40% (0.0040) of the values of Z fall greater than the value:
a. none of the other answers are correct
b. -1.19
c. 2.65
d. 3.14
e. -0.45
11. In the past the number of pages in science fiction books has had a normal distribution with a standard
deviation of 25. You are trying to support the hypothesis that the average number of pages of all book
exceeds 450. From a random sample of 25 books, you find a sample mean of 455 pages, what can you
conclude at a 5% level of significance?
a. not enough information is given to make a conclusion
b. We can say that the average number of pages does exceed 450
c. We can not say that the average number of pages exceeds 450
d. We can say that average number of pages equals 450
e. We can say the sample average is 450
12. How many observations do you need to collect to estimate the population average to within 0.1 feet
with 90% confidence? The population standard deviation was 1 foot. Use 95% confidence.
a. none of the other answers are correct
b. 3154
c. 271
d. 1.96
e. can not be solved
13. As the sample size gets larger the sampling distribution of the sample mean approaches:
a. the sound barrier (hint: very unsound choice).
b. a binomial distribution
c. the t distribution
d. a normal distribution
e. np and n(1-p)
14. Find Pr(-1.77 < Z < 2.79)
a. none of the others are correct
b. 0.9590
c. 0.5691
d. 1.2342
e. 0.0358
15. What course is this?
a. Insomnia zzzz
b. STAT 3321 (Hint: this one is a good choice)
c. STAT 3322
d. Rocket Science 8475
e. Sadistics 101
16. When using the sample mean to estimate the population mean, the margin of error is
a. the difference between the observed and hypothesized value in number of standard errors.
b. the standard deviation divided by the sample size
c. the probability that the mean will take on the value in the null hypothesis but still be wrong.
d. not really all that important (-10,000,001 points if you choose this one)
e. a multiple of the standard error.
17. What are the three terms in an alternative hypothesis?
a. the population parameter, the equal sign and a value
b. the sample mean, the standard error and the distribution
c. the sample mean, the population mean, and the population standard deviation
d. the population parameter, the direction (>, < or ≠) and a value
e. the sample mean, the equal sign, and a value
18. The values of the sample mean and their probabilities that result from taking random samples is called
a(n)
a. binomial distribution
b. sampling distribution
c. mean
d. median
e. standard deviation
19. What would be the rejection region when trying to support the alternative hypothesis that the
population mean is greater than 45? (The significance level is 0.05, the sample size is 51 and sigma is not
known)
a. impossible to determine with this information.
b. reject Ho if z > 2.05 or z < -2.05
c. reject Ho if t > 1.676
d. reject Ho if x differs from 45.
e. reject Ho if t < -1.645
20. Of the test statistics we have covered, each measure:
a. the temperature
b. the rejection region in number of t-table values times the standard deviation
c. the sample mean plus and minus the hypothesized value times the standard error of the mean
d. a non-measurement
e. the distance that the sample mean is from the hypothesized value in standard errors
21. A simple random sample
a. reduces bias
b. allows proportions to be the same as probabilities
c. is a requirement of all confidence intervals and hypothesis tests
d. all of the above are correct
e. none of the above are correct
22. Suppose the alternative hypothesis is “the average sales of a product is above 50”, a type I error is
a. concluding that the average sales is above 50 when it isn’t.
b. concluding the average sales could be 50
c. concluding that the average sales is less than 50 when it isn’t
d. concluding that the average sales could be 50 when it isn’t
e. the alternative hypothesis
23. If you wish to show that the average income in Arlington is above $45,000 using a hypothesis test, the
alternative hypothesis is
a. that the sample mean is greater than 45000
b. null hypothesis
c.  > 45,000
d. the type I error
e. that the sample mean is less than or equal to 44599
24. If the standard error of a sample mean is 4 and the population mean is 16, would a sample mean of 18
be unexpected?
a. Yes, because the standard error is much smaller than the population mean.
b. Hunh? (hint: very eloquent but still a poor choice)
c. No, because the value is less than what a typical error would be.
d. No, because the sample mean should have the same value as the population mean
e. Yes, because the population standard deviation is too large.
25. Given a normally distributed population with mean of 20 and standard deviation of 10, what is the
probability of finding a sample mean less than 21? (The sample size is 36.)
a. none of the others are correct
b. 1.6667
c. 0.7257
d. 0.2374
e. 0.6000
1. When applying the empirical rule to sample means, we center the sample means at the
population mean. See the textbook’s section on the Sampling Distribution of the Sample Mean
2. See hypothesis testing notes: Power is denoted as 
3. What you wish to support goes in the alternative hypothesis. The alternative hypothesis is used
to determine the rejection region. In this case you want to show that the mean > 98.6, therefore
the rejection region is right-sided.
4. Compute the z-score first. Z = (80-75)/10 = 0.5. Pr(Z > 0.50) = 0.3085 or 30.85%
5. for 95% use z values of ±1.96. The margin of error is ±1.96 times the standard error =
±1.96*(20) = ±39.2. You estimate the population mean to be 400 ± 39.2 = 400-39.2 up to 400 +
39.2. Therefore with 95% confidence, the average number of pages in all books falls between 360.8
and 439.2
6. Without knowing whether the IRS is correct or not, you can not be sure if the IRS has
correctly rejected the null hypothesis. This is either a Type I error or a correct decision

20
20

4
5
n
25
8. If you were not given information on the direction of the rejection region, then you would be
unable to determine the exact p-value. If
a. You have a right sided alternative and therefore a right-sided p-value, then find the pr( Z >
2.33 )=0.01
b. you have a left sided alternative, then find the Pr (Z < 2.33) = 0.99
c. you have a two sided test, determine Pr (Z > 2.33) and then double it. (0.02)
7. The standard error is

9. If you have a sample with three successes and two failures (S, S, S, F, F), then the proportion
of successes is 3/5. If you define a success to be a 1 and a failure to be a 0 (1,1,1,0,0) then the
average of those five numbers is also 3/5. So a proportion is a special case of a sample mean
where you are averaging one’s and zero’s.
10. Find the probability of 0.0040 in the greater than column and then see what value of Z
corresponds to it. You will find 2.65
11. You are trying to support  > 450 which goes in the alternative hypothesis making it a right
sided rejection region. At alpha of 0.05, the rejection region is Reject Ho if Z > 1.645 (Use a Z
because  is given). The standard error is 25 divided by the square root of 25 or the standard
error is 5. The distance between the sample mean and the population mean (455-450) = 5 is only
one standard error above the hypothesized mean. Therefore we can not say that the average
exceeds 450.
12. Use the sample size formula (Z /m.o.e.)2 = (1.645* /0.10)2 = 271 (after rounding up)
13. This is the central limit theorem, see textbook.
14. Find the probability that Z < 2.79 and then subtract from that the probability that Z < -1.77
15. Duh
16. The margin of error is Z (or t) times that standard error, therefore the margin of error is some
multiple of the standard error.
17. An alternative hypothesis is of the form H1:  > 30 ( the population parameter, the direction
(>, < or ≠) and a value )
18. Definition of sampling distribution
19. This is a right sided rejection region since you wish to support that the population mean is >
45. It uses a t since s is unknown. The degrees of freedom are n-1 = 50. Go to the t-table in the
back of the book, row 50 and column 0.05, the value is 1.676. Therefore the rejection region is to
reject Ho is t > 1.676
20. The test statistics we cover try to determine if the distance the sample mean and the
hypothesized value is too far (in number of standard errors). If it is too far away and supports the
alternative we can reject the null hypothesis.
21. The first three choices are all correct. The first two choices comes from the original
discussion of random sampling and the third choice comes from the requirements of confidence
intervals and hypothesis tests.
22. A type I error is to reject a true null hypothesis or to say that the alternative is true when it
isn’t. The alternative is that the average is above 50.
23. What you wish to support goes in the alternative and we wish to support that the population
mean is greater than 45.000
24. The typical error is 4. The observed sample mean is only 2 away from the population mean
(18-16). Therefore the value of the sample mean is not atypical and could have occurred under a
population mean of 16.
25. The standard error is 10 divided by the square root of 36 = 1.66667. The z value
corresponding to 21 is 0.6000. Pr ( sample mean is less than 21) = pr (Z < 0.60) = 0.7257