Project #20732 - stats

  1. 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

page1image21560
page1image21832
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Site where 3-5 year old children were sampled

Number of children with diagnosable malnutrition

page1image26656 page1image27080

Sample size

page1image29056

Head Start (public preschool programs)

page1image30472
page1image31160

49

page1image32536
page1image33128

384

page1image34928

Growing Places (private preschool)

page1image36704

6

81

page1image39888
page1image40424
page1image40704

Family Resource Center Public Clinic (free public health clinic)

page1image42576

21

page1image43960 page1image44552

241

page1image45816

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.

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Sample size (n)

Level of significance (α)

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Direction of the test

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Calculated value of t

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Critical value of t

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Decision about the null (reject or fail to reject)?

28

.05

page2image33808

Two-tailed

page2image35184
page2image35880

2.068

page2image37256
page2image37944
page2image38760
page2image39048 page2image39744

18

.05

One-tailed (right tail)

2.550

   

37

.001

Two-tailed

2.122

  page2image55968 page2image56664

7

.01

One-tailed (left tail)

page2image62208

-3.219

page2image63720
page2image64664
page2image65216

14

page2image66608

.05

page2image68672
page2image69216

One-tailed (left tail)

2.398

  page2image74200

Subject Mathematics
Due By (Pacific Time) 01/11/2014 11:00 pm
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