Question

C-reactive protein (CRP) is a substance that can be measured in the blood. Values increase substantially within 6 hours of an infection and reach a peak within 24 to 48 hours after. In adults, chronically high values have been linked to an increased risk of cardiovascular disease. In a study of apparently healthy children aged 6 to 60 months in Papua New Guinea, CRP was measured in 90 children. The units are milligrams per liter (mg/l). Here are the data from a random sample of 40 of these children. 0.00 10.83 14.68 9.29 0.00 20.07 26.23 12.37 32.13 0.00 74.59 0.00 48.13 0.00 0.00 23.92 10.83 0.00 0.00 4.67 0.00 0.00 14.68 9.29 14.68 0.00 21.61 0.00 58.08 20.07 6.21 0.00 0.00 0.00 0.00 13.14 16.22 23.15 20.84 6.21

(a) Look carefully at the data above. Do you think that there are outliers or is this a skewed distribution?

The distribution is skewed to the left, with a few high outliers.

The distribution is skewed to the right, with many high outliers.

The distribution is skewed to the left, with many high outliers.

The distribution is skewed to the right, with a few high outliers.

Now use a histogram or stemplot to examine the distribution. (Do this on paper. Your instructor may ask you to turn this in.)

(b) Do you think that the mean is a good characterization of the center of this distribution? Explain why or why not.

Yes. The mean is always a good measure of center.

No. The mean should never be used for distributions with outliers.

No. The mean is not the best measure of center for a skewed distribution. none of the above

(c) Find a 95% confidence interval for the mean CRP. (Round your answers to two decimal places.)

Lower limit

Upper limit

Discuss the appropriateness of using this methodology for these data.

The outliers make this methodology somewhat suspect.

The skewness makes this methodology somewhat suspect.

This method is appropriate for these data.

Answer 1

a.

From the above histogram it is clear that "The distribution is skewed to the right, with a few high outliers"

Answer is d).

b.

Yes, The mean is always a good measure of center

c.

From the data,

Since, the data is not normal, so t distribution is use here.

Confidence level = .95, so and degree of freedom = n-1 = 40-1 =39

Critical t value at 0.05 level of significance for 39 degree of freedom is 2.02

95% confidence interval for population mean is,

Lower limit : 7.44

Upper limit: 18.16