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 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 |
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 t-distribution 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)
f.)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 α = 0.05 (8 points)
2.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 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 |
3.The standard deviation of a normally distributed population is equal to 10. A sample size of 25 is selected, and its mean is found to be 95.
a.) Find an 80% confidence interval for μ. (4 points)
b.) If the sample size were 100 what would be the 80% confidence interval? (4 points)
c.) If the sample size was 25 but the standard deviation was 5, what would be the 80% confidence interval? (4 points)
4.We are interested in estimating the mean life of a new product. How large a sample do we need to take in order to estimate the mean to within 1/10 of a standard deviation with 90% confidence? (6 points)
5.The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of childcare to be $689. Assume the population standard deviation to be $40.
a.)Perform the appropriate test of hypothesis for the potential resident using α = 0.01. (8 points)
b.)Find the p-value for the test in a.). (3 points)
c.)What effect, if any, would there be on the conclusion in part a.) if you change α to 0.05? (3 points)
d.)Find the power of the test when μ is actually $685 and α = 0.05. (8 points)
Subject | Mathematics |
Due By (Pacific Time) | 07/31/2014 09:00 pm |
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