APStatistics

Unit 11 Inference for Distributions Free Response

Directions: Complete the assignment on this paper. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit.

1. Some students that attend college students work full or part time. How much did your working college friends each earn last month? Listed below is the amount earned last month by each student in a random sample of 35 college students.

0

0

105

0

313

453

769

415

244

0

333

0

0

362

276

158

409

0

0

534

449

281

37

338

240

0

0

0

142

0

519

356

280

161

0

1. Describe the population of interest. (2 points)
6. How many of the students in the sample worked last month? (2 points)
10. Describe the variable, amount earned by a working college student last month, using one graph, one measure of central tendency, and one measure of dispersion. (6 points)
20. Find evidence to show that the assumptions used for the Student's t-distribution have been satisfied. (2 points)
27. Estimate the mean amount earned by a college student per month using a point estimate and a 95% confidence interval. (4 points)
34. Based on records from the US Department of Education it is estimated that college students earn an average of $350. Does the sample show sufficient reason to reject the claim? Use ? = 0.05 (8 points)
44. What is the key difference between a 1-sample t-test and a 1-sample z-test?(4 points)
55. A shoe company wants to compare two materials (A and B) for use on the soles of boys' shoes. Now, you would expect certain variability among boys - some boys wear out shoes much faster than others. A problem arises if this variability is large. It might completely hide an important difference between the two materials. Suppose we give each randomly selected boy a special pair of shoes with the sole on one shoe made from material A and the other from material B. This procedure produced the data in the table below: (the measured data represents the height of the sole in millimeters.) Is there enough evidence to show that Material B is better than Material A? (12 points)

Boy

Material A

Material B

1

13.2

14.0

2

8.2

8.8

3

10.9

11.2

4

14.3

14.2

5

10.7

11.8

6

6.6

6.4

7

9.5

9.8

8

10.8

11.3

9

8.8

9.3

10

13.3

13.6

1. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4.21, and a standard deviation of 1.4. The second group consists of 20 subjects, has a sample mean of 3.15, and a standard deviation of 1.8. Test the null hypothesis that there is no difference between the population means of the two groups at the .01 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis. (6 points)
2. a.)
4. b.)
6. c.)
9. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4, and a variance of 5. The second group consists of 10 subjects, has a sample mean of 6, and a variance of 9. Test the null hypothesis that there is no difference between the population means of the two groups at the .10 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis. (6 points)

a.)

b.)

c.)

APStatistics Unit 11 Inference for Distributions Free Response Directions: Complete the assignment on this paper. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. 1. Some students that attend college students work full or part time. How much did your working college friends each earn last month? Listed below is the amount earned last month by each student in a random sample of 35 college students. 0 415 276 281 142 0 244 158 37 0 105 0 409 338 519 0 333 0 240 356 313 0 0 0 280 453 0 534 0 161 769 362 449 0 0 a.) Describe the population of interest. (2 points) b.) How many of the students in the sample worked last month? (2 points) c.) Describe the variable, amount earned by a working college student last month, using one graph, one measure of central tendency, and one measure of dispersion. (6 points) d.) Find evidence to show that the assumptions used for the Student's tdistribution have been satisfied. (2 points) e.) Estimate the mean amount earned by a college student per month using a point estimate and a 95% confidence interval. (4 points) 2. Based on records from the US Department of Education it is estimated that college students earn an average of $350. Does the sample show sufficient reason to reject the claim? Use = 0.05 (8 points) 3. What is the key difference between a 1sample ttest and a 1sample ztest?(4 points) 4. A shoe company wants to compare two materials (A and B) for use on the soles of boys' shoes. Now, you would expect certain variability among boys some boys wear out shoes much faster than others. A problem arises if this variability is large. It might completely hide an important difference between the two materials. Suppose we give each randomly selected boy a special pair of shoes with the sole on one shoe made from material A and the other from material B. This procedure produced the data in the table below: (the measured data represents the height of the sole in millimeters.) Is there enough evidence to show that Material B is better than Material A? (12 points) Boy 1 2 3 Material A 13.2 8.2 10.9 Material B 14.0 8.8 11.2 4 5 6 7 8 9 10 14.3 10.7 6.6 9.5 10.8 8.8 13.3 14.2 11.8 6.4 9.8 11.3 9.3 13.6 5. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4.21, and a standard deviation of 1.4. The second group consists of 20 subjects, has a sample mean of 3.15, and a standard deviation of 1.8. Test the null hypothesis that there is no difference between the population means of the two groups at the .01 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis. (6 points) a.) b.) c.) 6. A researcher collects data on two independent samples. The first group consists of 20 human subjects, has a sample mean of 4, and a variance of 5. The second group consists of 10 subjects, has a sample mean of 6, and a variance of 9. Test the null hypothesis that there is no difference between the population means of the two groups at the .10 level of significance. Indicate a) the observed value of the test statistic, b) the critical value(s), c) whether you reject or fail to reject the null hypothesis. (6 points) a.) b.) c.)