# PHE5IST Biostatistics

## Question:

Below are estimates of the daily intake of calcium (in milligrams) for 38 women between the ages of 51 and 80 years who participated in a study of women’s bone health:
808 882 1062 970 909 802 374 416 784 997
651 716 438 1420 1525 948 1050 976 572 403
626 774 1253 549 1325 446 465 1769 671 696
1156 684 1933 748 1203 2433 1255 1100
a. Using the above histogram describe the distribution of calcium intakes for these women.
b. Calculate the mean, median, range, standard deviation, variance and the standard error.
c. Find a 95% confidence interval for the mean. Interpret this confidence interval.
d. Suppose that the recommended daily allowance (RDA) of calcium for women in this age is 1200 milligrams (this value is changed from time to time on the basis of the statistical analysis of new data). Express the mean and median of the results from b in terms of percent of the RDA.
e. Divide each intake by the RDA, multiple by 100, and compute the 95% confidence interval from the transformed data.
f. Verify that you can obtain the same results by similarly transforming the interval you calculated in c.

A rare congenital disease, Everley's syndrome, generally causes a reduction in concentration of blood sodium. This is thought to provide a useful diagnostic sign as well as a clue to the efficacy of treatment. Over the course of seven years, 20 cases of Everley’s syndrome were diagnosed at a London teaching hospital. The patients were all aged
between 20 and 44 and agreed to take part in an experimental treatment program.At diagnosis, the blood sodium levels of these 20 cases were:
110 95 120 112 106 109 98 152 111 105
96 97 114 116 87 142 95 111 120 122

a. Assuming that blood sodium concentration is normally distributed what is the 95% confidence interval within which the mean of the total population of such cases may be expected to lie.
After 12 months of the experimental treatment program, the blood sodium levels of these 20 cases were (in order):
108 126 119 106 116 122 114 148 120 110
127 142 130 126 114 134 121 135 120 126
b. Is the experimental method of treatment effective at raising the blood sodium levels of patients with Everley’s syndrome Justify your answer using statistical methods and language.

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