STAT 240 Quiz 6 KEY
1. In a national survey conducted in 2000, the National Opinion Research Center asked a random sample
of 1,780 adults whether they favored or opposed the legalization of marijuana. A total of 1,183, or
roughly 65.5%, of the respondents said they were opposed to legalization. The researchers want to
estimate the national proportion that is opposed. . What method should the researchers use to estimate the
proportion of the population opposed to legalization?
A. Confidence interval for one mean
B. Confidence interval for the difference between two means
C. Confidence interval for one proportion
D. Confidence interval for difference between two proportions
Questions 2-3. A null hypothesis is that the mean nose lengths of men and women are the same. The
alternative hypothesis is that men have a larger nose length than women.
2. Which of the following is the correct way to state the null hypothesis?
A. x 1  x 2  0
B. x1  x 2  0
C. 1 2  0
D. 1 2 = 0
3. A statistical test is done and the p-value is 0.339. Which of the following is the most correct way to
appropriately state the conclusion?
A. The mean nose lengths of men and women are identical
B. Men have a greater mean nose length.
C. The probability is 0.339 that men and women have the same mean nose length.
D. There is not enough evidence to say that that men and women have different nose lengths.
-------------------------------------------------------------------------4. A psychiatrist examining treatments for depression declares that a new treatment is better than a
standard treatment. The null hypothesis was that the new treatment was not better; the alternative
hypothesis was that the new treatment was better. Which statement is correct?
A. The psychiatrist may have made a Type 1 error
B. The psychiatrist may have made a Type 2 error
5. Consider comparing two population means. Which one of these statements about the power of a
significance test is FALSE?
A. The greater the true difference (the effect size), the larger the power.
B. The power of a test is the probability of a Type 2 error
C. The larger the sample size, the greater the power of significance test.
D. The power of a test is affected by the level of significance used.
6. An agricultural experiment will be done to compare the effectiveness of two different soil treatments.
Which of the following sample sizes gives the greatest risk that a Type 2 error will be made?
A. n = 400 B. n = 100
C. n = 20
D. n = 10
7.. Which of the following is an incorrect way to state a null hypothesis?
A. H0: p̂1  p̂ 2  0
B. H0: d = 0
C. H0:  1   2 = 0
D. H0: p 1  p 2  0
8. When comparing two means, the situation most likely to lead to a statistically significant result that
has little practical importance is
A. when the true difference is large and the sample sizes are small.
B. when the true difference is small and the sample sizes are large.
C. when the true difference is small and the sample sizes are small.
Questions 9 and 10: For the variable “Time spent watching TV in Typical Day,” here are results of a
two-sample t-procedure that compares a random sample of women (group 1) and men (group 2) at a
college.
Sex
N
Mean
StDev
SE Mean
f
116
1.95
1.51
0.14
m
59
2.37
1.87
0.24
95% CI for mu (f) - mu (m): ( -0.97, 0.14)
T-Test mu (f) = mu (m) (vs not =): T = -1.49 P = 0.14 DF = 97
9. According to the output, what is the alternative hypothesis of the t-test?
A. 1 = 2 B. 1  2
C. 1 > 2
D. 1 < 2
10. Which of the following is the correct conclusion about these results?
A. There is a statistically significant difference observed between the mean TV watching times
of men and women.
B. There is not a statistically significant difference observed between the mean TV
watching times of men and women.
------------------------------------11. A question in a survey of college students is, “Would you tell if you cheated on a significant other
(Yes or No)?” A group of students analyzes the data to determine if females are more likely to say “yes”
than males. What is the appropriate parameter for the students to analyze?
A. value of one proportion
B. difference between two proportions
C. value of one mean
D. difference between two means
12. Refer to the previous question. What technique should be used to determine if females are more
likely than males to say “yes?”
A. Confidence interval
B. Hypothesis test
13. A null hypothesis is H0: 1 2 = 0 and the alternative hypothesis is the one-sided Ha: 1  2 > 0.
Suppose a 90% confidence interval for the difference 1 2 is computed. Is the following sentence true
or false? We can reject H0 at the  = .05 significance level if the 90% confidence interval is entirely
above 0.
A. True
B. False
14. Which of the following is a likely difficulty caused by a small sample size?
A.
A small unimportant difference might be declared to be statistically significant
B.
We may fail to find an actual difference because the power is too low.
C.
There is a high risk of a type 1 error.
D.
The confidence level for a confidence interval could be too low.
15. A researcher asked random samples of 25 waitresses and 25 female lawyers if they had experienced
sexual harassment on the job in the previous month (Yes, No, Not sure). A 95% confidence interval
for p1  p2 is 0.03 to 0.53, where p1 and p2 are the population proportions for waitresses and female
lawyers, respectively, who would answer "yes" to the question if asked. Based on this result, it is
reasonable to conclude that ____
A. Waitresses and female lawyers don't experience sexual harassment.
B. Waitresses and female lawyers experience equal amounts of sexual harassment.
C. Female lawyers are more likely to experience sexual harassment than are waitresses.
D. Waitresses are more likely to experience sexual harassment than are female lawyers.