Confidence intervals
1. You are working on a research project examining the extent of protein-energy malnutrition among preschool aged children in the greater Manchester, NH area. As part of this project, you will need to use the following data (Table 1).
TABLE 1.
1a. Estimate the 95% confidence interval for the proportion of children at each site who were malnourished. Show all calculations for partial credit.
1b. Interpret fully what these intervals tell you, then determine if there are significant differences in the levels of malnutrition in the populations of children at each site?
1c. Now suppose that the NH Department of Public Health data show you that 7% of three to five year olds in the entire state are malnourished. How do your three samples differ, if at all, from the state average?
1d. You are asked by your supervisor to draft a statement about how funds for supplemental nutrition programs should be spent. Using the raw data and your calculations to support your case, what recommendations would you make?
Z-scores
Site where 3-5 year old children were sampled |
Number of children with diagnosable malnutrition |
Sample size |
Head Start (public preschool programs) |
49 |
384 |
Growing Places (private preschool) |
6 |
81 |
Family Resource Center Public Clinic (free public health clinic) |
21 |
241 |
2
2. A survey of 708 people who graduated from college in 2013 had an average student load debt of $35,200 (s.d. = $12,800).
2a. Calculate the percentile rank of a recent graduate who graduated with $48,000 in education-related debt. Show your work for partial credit.
2b. To qualify for an experimental loan repayment program with a lower interest rate, borrowers have to be within the 65th to 75th percentiles of debt. Sally has a total educational debt of $54,912. Would she be an acceptable candidate for this program? Show work for partial credit.
2c. Borrowers who have excessive debt levels (in the 85th percentile or higher) are more likely to default on their loans. What debt value would mark this amount? Show work for partial credit.
One- sample t-tests
3. A random sample of 92 sociology majors who graduated in 2010 was drawn from three colleges and universities in New England. Six months after graduation, all 92 people were employed. They had a mean salary of $28,834 (s.d.= $7,095). Figures from the National Association of Colleges and Universities, however, shows that the nationwide average starting salary for degree recipients in sociology was $30,000. Is your sample’s mean salary significantly different from the population? Show all work for partial credit.
4. Complete the following table, which presents the results of a series of t-tests, with varying sample sizes and levels of significance. For each test, find the critical value, the p-value at which this test is significant, and whether you would reject or fail to reject the null hypothesis.
TABLE 2.
Sample size (n) |
Level of significance (α) |
Direction of the test |
Calculated value of t |
Critical value of t |
Decision about the null (reject or fail to reject)? |
28 |
.05 |
Two-tailed |
2.068 |
||
18 |
.05 |
One-tailed (right tail) |
2.550 |
||
37 |
.001 |
Two-tailed |
2.122 |
||
7 |
.01 |
One-tailed (left tail) |
-3.219 |
||
14 |
.05 |
One-tailed (left tail) |
2.398 |
Subject | Mathematics |
Due By (Pacific Time) | 01/11/2014 11:00 pm |
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