Normal distribution - Confidence Interval, P-value, Margin of Error, Hypothesis Testing: Exercise 7-1 to Exercise 9-4 select questions
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normaldistribution_questions.docExercise 7-1
Q # 10
Number of faculty. the numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence. assume .
|
211 |
384 |
396 |
211 |
224 |
337 |
395 |
121 |
356 |
|
621 |
367 |
408 |
515 |
280 |
289 |
180 |
431 |
176 |
|
318 |
836 |
203 |
374 |
224 |
121 |
412 |
134 |
539 |
|
471 |
638 |
425 |
159 |
324 |
|
|
|
|
Q # 14
Number of jobs. a sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. the population standard deviation is 2.1.
a. find the best point to estimate of the population men.
b.find the 95 % confidence interval of the mean number of jobs.
c.find the 99% confidence interval of the mean number of jobs.
d. which is smaller? explain why.
Q # 18
Day care tuition. a random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. find the 90% confidence interval of the true mean. if a day care center were starting up and wanted to keep tuition low. what would be a reasonable amount to charge?
Exercise 7-2
Q # 8
State Gasoline Taxes. a random sample of state gasoline taxes ( in cents ) is shown here for 12 states. use the data to estimate the true population mean gasoline tax with 90% confidence. does your interval contain the national average of 44.7 cents?
|
38.4 |
40.9 |
67 |
32.5 |
51.5 |
43.4 |
|
38 |
43.4 |
50.7 |
35.4 |
39.3 |
41.4 |
Q # 10
Dance Company Students. the number of students who belong to dance company at each of several randomly selected small universities is shown below. estimate the true population mean size of a university dance company with 99% confidence.
|
21 |
25 |
32 |
22 |
28 |
30 |
29 |
30 |
|
47 |
26 |
35 |
26 |
35 |
26 |
28 |
28 |
|
32 |
27 |
40 |
|
|
|
|
|
Exercise 7-3
Q # 6
Belief in haunted places. a random sample of 205 college students were asked if they believed that places could be haunted, and 65 responded yes. estimate the true proportion of college students who believed in the possibility of haunted places with 99% confidence. according to time magazine,37% of americans believe that places can be haunted.
Q # 14
Fighting U.S hunger. in a poll of 1000 likely voters, 560 say that the united states spends too little on fighting hunger at home. find a 95% confidence interval for the true proportion of voters who feel this way.
Exercise 8-2
Q # 4
Moviegoers. the average moviegoer sees 8.5 movies a year. a moviegoer is defined as a person who sees at least one movie in a theater in a 12 month period. a random sample of 40 moviegoers from a large university revealed that the average number of movies seen per person was 9.6. The population standard deviation is 3.2 movies. at the 0.05 level of significance, can it be concluded that this represents a difference from the national average?
Q # 8
Salaries of government employees. the mean salary of federal government employees on the general schedule is $59,593. the average salary of 30 state employees who do similar work is $58,800 with . at the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees?
Q # 12
Student expenditures. the average expenditure per student ( based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. a survey for the next school year of 150 randomly selected students resulted in a sample mean of $10,798. do these results indicates that the average expenditure has changed? choose your own level of significance.
Exercise 8-3
Q # 6
Park acreage. a state executive claims that the average number of acres in western pennsylvania state parks is less that 2000 acres. a random sample of five parks is selected, and the number of acres is shown. at , is there enough evidence to support the claim?
|
959 |
1187 |
493 |
6249 |
541 |
Q # 14
Chocolate chip cookie calories. the average 1-ounce chocolate chip cookie contains 110 calories. a random sample of 15 different brands of 1-ounce chocolate chip cookies resulted in the following calorie amounts. at the , is there sufficient evidence that the average calorie content is greater than 110 calories?
|
100 |
125 |
150 |
160 |
185 |
125 |
155 |
145 |
160 |
|
100 |
150 |
140 |
135 |
120 |
110 |
|
|
|
Exercise 8-4
Q # 8
Female Physicians. the percentage of physicians who are women is 27.9%. in a survey of physicians employed by a larger university health system,45 of 120 randomly selected physicians were women. is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians at the university health system exceeds 27.9%?
Q # 18
Doctoral student's salaries. nationally, at least 60% of Ph.D. Students have paid assistantship. a college dean feels that this is not true in his state, so he randomly selected 50 Ph.D. Students and finds that 26 have assistantships. at , is the dean correct?
Exercise 9-1
Q # 6
Teachers salaries. california and new york lead the list of average teacher's salaries. the california yearly average is $64,421 while teachers in new york make an average annual salary of $62,332. random samples of 45 teachers from each state yielded the following
|
|
California |
New York |
|
Sample mean |
64,510 |
62,900 |
|
Population standard deviation |
8,200 |
7,800 |
at is a difference in means of the salaries?
Q # 10
Home Prices. a real estate agent compares the selling prices of homes in two municipalities in south western pennsylvania to see if there is a difference. the results of the study are shown. is there enough evidence to reject the claim that the average cost of a home in both locations is the same? use .
|
Scott |
Ligonier |
|
$93,430* |
$98,043* |
|
$5602 |
$4731 |
|
35 |
40 |
Q # 16
Ages of College Students . the dean of students wants to see whether there is a significant difference in ages of resident students and commuting students. she selects a sample of 50 students from each group. the ages are shown here. at ,decide if there is enough evidence to reject the claim of no difference in the ages of the two groups. use the P-value method. assume
and
Resident Students
|
22 |
25 |
27 |
23 |
27 |
28 |
26 |
24 |
|
25 |
20 |
26 |
24 |
27 |
26 |
18 |
19 |
|
18 |
30 |
26 |
18 |
18 |
19 |
32 |
23 |
|
19 |
19 |
18 |
29 |
19 |
22 |
18 |
22 |
|
26 |
19 |
19 |
21 |
23 |
18 |
20 |
18 |
|
22 |
21 |
19 |
21 |
21 |
22 |
18 |
20 |
|
19 |
23 |
|
|
|
|
|
|
Commuter Students
|
18 |
20 |
19 |
18 |
22 |
25 |
24 |
35 |
|
23 |
18 |
23 |
22 |
28 |
25 |
20 |
24 |
|
26 |
30 |
22 |
22 |
22 |
21 |
18 |
20 |
|
19 |
26 |
35 |
19 |
19 |
18 |
19 |
32 |
|
29 |
23 |
21 |
19 |
36 |
27 |
27 |
20 |
|
20 |
21 |
18 |
19 |
23 |
20 |
19 |
19 |
|
20 |
25 |
|
|
|
|
|
|
Exercise 9-3
Q # 2
Retention test scores. a sample of non-english majors at a selected college was used in a study to see if the student retained more from reading a 19th century novel or by writing it in DVD form. each student was assigned one novel to read and a different one to watch, and then they were given a 100-point written quiz on each novel. the test results are shown below. at , can it be concluded that the book scores are higher than the DVD scores?
|
Book |
90 |
80 |
90 |
75 |
80 |
90 |
84 |
|
DVD |
85 |
72 |
80 |
80 |
70 |
75 |
80 |
Q # 4
Obstacle course times. an obstacle course was set up on a campus, and 10 volunteers were given a chance to complete it while there were being time. they then sampled a new energy drink and were given the opportunity to run the course again. the before and after times in seconds are shown below. is there sufficient evidence at to conclude that the students did better the second time? discuss possible reasons for your results.
|
Student |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Before |
67 |
72 |
80 |
70 |
78 |
82 |
69 |
75 |
|
After |
68 |
70 |
76 |
65 |
75 |
78 |
65 |
68 |
Q # 10
A random sample of six music students played a short song, and the number of mistakes each student made was recorded. after they practiced the song 5 times, the number of mistakes each student made was recorded. the data are shown. at , can it be concluded that there was a decrease in the mean number of mistakes?
|
Student |
A |
B |
C |
D |
E |
F |
|
Before |
10 |
6 |
8 |
8 |
13 |
8 |
|
After |
4 |
2 |
2 |
7 |
8 |
9 |
Exercise 9-4
Q # 4
Undergraduate financial aid. a study is conducted to determine if the percent of women who receive financial aid in undergraduate school is different from the percent of men who receive financial aid in undergraduate school. a random sample of undergraduates revealed these results. at , is there significant evidence to reject the null hypothesis?
|
|
Women |
Men |
|
Sample Size |
250 |
300 |
|
Number receiving aid |
200 |
180 |
