Instructor: Doug Ensley
Course: MAT117 01 Applied Statistics Assignment: Online 13 ­ Section 10.1
­ Ensley
Student: _____________________
Date: _____________________
1. According to a study, the official unemployment rate was 15.5% among Blacks and 7.9% among Whites as of March 2011. During the recession of 2009­2011, the Black levels of unemployment have been similar or in many locations higher than those during the Great Depression era. Complete parts a through c below.
a. Identify the response variable and the explanatory variable.
The response variable is (1) and the explanatory variable is (2) b. Identify the two groups that are the categories of the explanatory variable.
Race and unemployment rate
Employed and unemployed individuals
Black and white individuals
c. The unemployment statistics are based on a sample of individuals. Were the samples of white individuals and black individuals independent samples, or dependent samples?
A. The samples were dependent because no individuals could be in both samples. B. The samples were dependent because individuals could be in both samples. C. The samples were independent because individuals could be in both samples. D. The samples were independent because no individuals could be in both samples. (1)
unemployment rate
race
(2)
race.
unemployment rate.
2. Random samples of students at 117 four­year colleges were interviewed several times since 1993. Of the students who reported drinking alcohol , the percentage who reported drinking to get drunk was 48.3 % of 12,078 students in 1993 and 42.4% of 9207 students in 2004.
a. Estimate the difference between the proportions in 2004 and 1993 , and interpret.
b. Find the standard error for this difference.
c. Construct and interpret a 95 % confidence interval to estimate the true change.
d. State the assumptions for the confidence interval in (c) to be valid.
a. Estimate the difference between the proportions in 2004 and 1993.
(Round to three decimal places as needed.)
Interpret this estimate. Choose the sentence below that best describes the estimate between 1993 and 2004.
A. The proportion appears to have decreased from 1993 to 2004.
B. The proportion appears unchanged from 1993 to 2004.
C. The proportion appears to have increased from 1993 to 2004.
b. What is the standard error for this difference?
se =
(Round to four decimal places as needed.)
c. Construct a 95 % confidence interval for the difference between the population proportions from 1993 to 2004.
(
,
) (Round to three decimal places as needed.)
Interpret the 95 % confidence interval.
A. There is evidence that the true proportion increased from 1993 to 2004.
B. There is evidence that the true proportion decreased from 1993 to 2004.
C. There is no evidence that the true proportion changed from 1993 to 2004.
d. What assumptions are necessary for the confidence interval to be valid?
A. Both samples must include the same students.
B. Both samples must be selected from a population that is approximately normal.
C. Both samples must be independent, random, and large enough.
D. Both samples must be independent and p must be close to p .
1
2
3. A survey of 32,739 adults in 1999 indicated that 28.5 % of adults were current smokers. A similar study conducted in 1995 of 46,000 adults indicated that 21.8% were current smokers.
a. Find and interpret a point estimate of the difference between the proportion of current smokers in 1995 , and the proportion of current smokers in 1999.
b. A 95 % confidence interval for the true difference is (0.061,0.073). Interpret.
c. What assumptions must you make for the confidence interval in part b to be valid?
a. Find a point estimate of the difference between the proportion of current smokers in 1995 and the proportion of current smokers in 1999.
(Round to three decimal places as needed.)
Interpret this point estimate. Choose the correct answer below.
A. The proportion of current smokers appears to be unchanged from 1995 to 1999.
B. The proportion of current smokers appears to have increased from 1995 to 1999.
C. The proportion of current smokers appears to have decreased from 1995 to 1999.
b. Interpret the 95 % confidence interval (0.061,0.073). Choose the correct answer below.
A. There is no evidence that the true proportion changed from 1995 to 1999.
B. There is evidence that the true proportion increased from 1995 to 1999.
C. There is evidence that the true proportion decreased from 1995 to 1999.
c. What assumptions are necessary for the confidence interval to be valid?
A. Both samples must be independent, random, and large enough.
B. Both samples must include the same students.
C. Both samples must be selected from a population that is approximately normal.
D. Both samples must be independent and p must be close to p .
1
2
4. A survey of 32,566 adults in 2001 indicated that 27.9 % of adults were current smokers. A similar study conducted in 1992 of 45,000 adults indicated that 24.4% were current smokers.
a. Find and interpret a point estimate of the difference between the proportion of current smokers in 1992 , and the proportion of current smokers in 2001.
b. A 95 % confidence interval for the true difference is (0.029,0.041). Interpret.
c. What assumptions must you make for the confidence interval in part b to be valid?
a. Find a point estimate of the difference between the proportion of current smokers in 1992 and the proportion of current smokers in 2001.
(Round to three decimal places as needed.)
Interpret this point estimate. Choose the correct answer below.
A. The proportion of current smokers appears to have increased from 1992 to 2001.
B. The proportion of current smokers appears to have decreased from 1992 to 2001.
C. The proportion of current smokers appears to be unchanged from 1992 to 2001.
b. Interpret the 95 % confidence interval (0.029,0.041). Choose the correct answer below.
A. There is no evidence that the true proportion changed from 1992 to 2001.
B. There is evidence that the true proportion decreased from 1992 to 2001.
C. There is evidence that the true proportion increased from 1992 to 2001.
c. What assumptions are necessary for the confidence interval to be valid?
A. Both samples must be independent, random, and large enough.
B. Both samples must be independent and p must be close to p .
1
2
C. Both samples must be selected from a population that is approximately normal.
D. Both samples must include the same students.
5. A study used 1327 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. The table shows a technology output, where X is the number of deaths due to heart attack during a follow­up period of about 3 years. Sample 1 received the placebo and sample 2 received aspirin. Complete parts a through d below.
1
Click the icon to view the technology output.
a. Explain how to obtain the values labeled "Sample p." Choose the correct answer below.
A. "Sample p" is the sample proportion, p, where p =
n
x
.
B. "Sample p" is the sample proportion, p, where p = p1 − p2 .
C. "Sample p" is the sample point, p, where p = n − x.
D. "Sample p" is the sample proportion, p, where p =
x
n
.
b. Explain how to interpret the value given for "estimate for difference." Choose the correct answer below.
A.
The estimate for difference given suggests that taking aspirin increases the risk of death from a heart attack for stro
victims.
B.
The estimate for difference given suggests that taking aspirin decreases the risk of death from a heart attack for stro
victims.
C.
The estimate for difference given suggests that taking aspirin does not affect the risk of death from a heart attack fo
victims.
c. Explain how to interpret the confidence interval, indicating the relevance of 0 falling in the interval.
How can the confidence interval be interpreted?
A. There is evidence that taking aspirin increases the risk of death from a heart attack for stroke victims.
B. There is not evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.
C. There is evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.
In general, what is the relevance of 0 falling in a confidence interval?
A. The population proportions might be equal.
B. The population proportions are small.
C. One of the population proportions is larger than the other.
D. There is no relevance of 0 falling in the confidence interval.
d. If sample 1 instead refers to the aspirin treatment and sample 2 the placebo treatment, explain how the estimate of the difference and the 95% confidence interval would change. Explain how then to interpret the confidence interval. (Note that the output given would change for the analysis of this difference.)
How would the estimate of the difference and the 95% confidence interval change?
A. The estimate of the difference would be 0.027519 and the confidence interval would be ( − 0.045462, − 0.009
B. The estimate of the difference would be − 0.027519 and the confidence interval would be (0.009576 ,0.04546
C. The estimate of the difference would be − 0.027519 and the confidence interval would be ( − 0.045462, − 0.0
D. The estimate of the difference and confidence interval would not change.
How can the new confidence interval be interpreted?
A. There is not evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.
B. There is evidence that taking aspirin increases the risk of death from a heart attack for stroke victims.
C. There is evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.
1: Deaths Due to Heart Attacks in Study
Sample
X
N
Sample p
1
28
659
0.042488619
2
10
668
0.01497006
Difference = p(1) − p(2)
Estimate for difference: 0.027519
95% CI for difference: (0.009576 ,0.045462 )
Test for difference = 0 (vs not = 0): z = 3 P­Value = 0.0027
1. (1) unemployment rate
(2) race.
Black and white individuals
D. The samples were independent because no individuals could be in both samples. 2. − 0.059
A. The proportion appears to have decreased from 1993 to 2004.
0.0069
− 0.072
− 0.046
B. There is evidence that the true proportion decreased from 1993 to 2004.
C. Both samples must be independent, random, and large enough.
3. 0.067
B. The proportion of current smokers appears to have increased from 1995 to 1999.
B. There is evidence that the true proportion increased from 1995 to 1999.
A. Both samples must be independent, random, and large enough.
4. 0.035
A. The proportion of current smokers appears to have increased from 1992 to 2001.
C. There is evidence that the true proportion increased from 1992 to 2001.
A. Both samples must be independent, random, and large enough.
5.
x
D. "Sample p" is the sample proportion, p, where p = .
n
B.
The estimate for difference given suggests that taking aspirin decreases the risk of death from a heart attack for stroke
victims.
C. There is evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.
A. The population proportions might be equal.
C.
The estimate of the difference would be − 0.027519 and the confidence interval would be ( − 0.045462, − 0.009576).
C. There is evidence that taking aspirin decreases the risk of death from a heart attack for stroke victims.