# Immunologic Study

5. Human body temperatures are normally distributed with a mean of 98.6 degrees F and a standard deviation of 0.72 deg. F. Find the temperature that separates the top 7% from the bottom 93%.

6. In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of skin test reaction to an antigen. The sample mean and sample standard deviation were 21 and 11 mm erythema, respectively. Can it be conducted from these data that the population mean is less than 30? Let alpha=0.05. Assume that the population standard deviation is 12.2

7. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed.

Before: 74 83 75 88 84 63 93 84 91 77

After: 73 77 70 77 74 67 95 83 84 75

Note: define d=before - after then mean of d=3.7 and s=4.95

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#### Solution Preview

5. This is a confidence interval question and is a one-tailed distribution: To construct the confidence interval of 93%, we should use the formula:

<br>Upper limit UL = M + z*s

<br>In this case, M=98.6, s=0.72 and z value at 0.93 is z=1.475

<br>Then UL = M + z*s=98.6+1.475*0.72=99.66 degrees F, which is the temperature that separates the top 7% from the bottom 93%.

<br>

<br>6. Since the population standard deviation is known, we'd better apply this to our calculation.

<br>This is ...

#### Solution Summary

The solution addresses human body temperatures are normally distributed with a mean of 98.6 degrees F and a standard deviation of 0.72 deg. F. Find the temperature that separates the top 7% from the bottom 93%.

6. In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of skin test reaction to an antigen. The sample mean and sample standard deviation were 21 and 11 mm erythema, respectively. Can it be conducted from these data that the population mean is less than 30? Let alpha=0.05. Assume that the population standard deviation is 12.2

7. A test of abstract reasonign is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed.

Before: 74 83 75 88 84 63 93 84 91 77

After: 73 77 70 77 74 67 95 83 84 75

Note: define d=before - after then mean of d=3.7 and s=4.95