1. 8 points) (Pagano/Gauvreaux Ch9 Q5) The distributions of systolic and diastolic blood pressures for female diabetics between the ages of 30 and 34 have unknown means. However, their standard deviations are 11.8 mmHg (for systolic) and 9.1 mmHg (for diastolic).

1. A random sample of 10 women is selected from this population. The mean systolic blood pressure for the sample is 130 mm Hg. Calculate a two-sided 95% confidence interval for the true mean systolic blood pressure, and interpret.

1. The mean diastolic blood pressure for the sample of size 10 is 84 mm Hg. Find a two-sided 90% confidence interval for the true mean diastolic blood pressure, and interpret.

1. Calculate a two-sided 99% confidence interval for mean diastolic blood pressure.

1. How does the 99% confidence interval compare to the 90% interval?

1. (8 points) (Pagano/Gauvreaux Ch9 Q6) Consider the t distribution with 5 degrees of freedom.

1. What proportion of the area under the curve lies to the right of 2.015?

1. What proportion of the area lies to the left of -3.365?

1. What proportion of the area lies between -4.032 and 4.032?

1. What value of t cuts off the upper 2.5% of the distribution?

1. (8 points) (Pagano/Gauvreau Ch9 Q9) For the population of infants subjected to fetal surgery for congenital anomalies, the distribution of gestational ages at birth is approximately normal with unknown mean and standard deviation. A random sample of 14 such infants has sample mean gestational age 29.6 wks and sample standard deviation 3.6 wks.

1. Construct a 95% confidence interval for the true population mean gestational age.

1. What is the length of this interval?

1. How large a sample would be required for the 95% confidence interval to have length 3 weeks? You can assume the population standard deviation is known to be 3.6 wks (i.e. use the normal distribution).

1. (8 points) (Pagano/Gauvreaux Ch 9 Q11) Eight individuals experienced an unexplained episode of vitamin D intoxication. Blood levels of calcium and albumin for each subject at the time of hospitalization are given below.

Calcium (mmol/l)	Albumin (g/l)
2.92	43
3.84	42
2.37	42
2.99	40
2.67	42
3.17	38
3.74	34
3.44	42

1. Construct a one-sided 95% confidence interval - a lower bound - for the true mean calcium level of individuals who experience vitamin D intoxication.

1. Compute a 95% lower confidence bound for the true mean albumin level of this group.

1. For healthy individuals, the normal range of calcium values is 2.12 to 2.74 mmol/l and the range of albumin levels is 32 to 55 g/l. Do you believe that patients suffering from vitamin D intoxication have normal blood levels of calcium and albumin?

1. (8 points) (Pagano/Gauvreaux Ch9 Q12) The data setlowbwtcontains information recorded for a sample of 100 low birth weight infants in two teaching hospitals in Boston. Measurements of systolic blood pressure are saved under the variable namesbp, and indicators of gender - 1 for male and 0 for female - are in the variablesex.

1. Compute a 95% confidence interval for the true mean systolic blood pressure of male low birth weight infants.

1. Compute a 95% confidence interval for the true mean systolic blood pressure of female low birth weight infants.

1. Do you think it is possible that males and females have the same mean systolic blood pressure? Explain briefly.

Useful STATA:

ci sbp if sex==1

ci sbp if sex==0, level(99) -- For this assignment you're only using the default level (95), but this is how you would change it if you wanted to.

1. (8 points) (Pagano/Gauvreaux Ch10 Q9) The distribution of diastolic blood pressures for the population of females diabetics between the ages of 30 and 34 has unknown mean and standard deviation 9.1 mm Hg. It may be useful for physicians to know whether the mean of this population is equal to the mean diastolic blood pressure for the general populations of females in this age group, 74.4 mm Hg.

1. State the hypotheses for an appropriate test.

1. A sample of 10 diabetic women is selected, and have sample mean 84 mm Hg. Conduct a two-sided test at the 0.05 significance level. What is the p-value of the test? State your conclusions.

1. Would your conclusion have been different if you had chosen a significance level of 0.01?

1. (8 points) (Pagano/Gauvreaux Ch10 Q10) E. canis infection is a tick-borne disease of dogs that is sometimes contracted by humans. Among infected humans, the distribution of white blood cell counts has unknown mean and standard deviation. In the general population, the white blood cell count is 7250/mm3. It is believed that infected persons must on average have lower white blood cell counts.

1. What are the hypotheses for a one-sided test?

1. For a sample of 15 infected persons, the sample mean is 4767 and the sample standard deviation is 3204. Conduct the test at the 0.05 significance level, and state your conclusions.

1. (8 points) (Pagano/Gauvreau Ch 10 Q 11) Body mass index is a measure of the extent to which an individual is overweight. For the population of middle-aged men who later develop diabetes mellitus, the distribution of baseline body mass indices is approximately normal with unknown mean and standard deviation. A sample of 58 men selected from this group has sample mean 25.0 kg/m2 and sample standard deviation 2.7 kg/m2.

1. Construct a 95% confidence interval for the population mean.

1. At the 0.05 significance level, test whether the mean baseline body mass index for the population of middle-aged men who develop diabetes is equal to 24.0 kg/m2 (this is the mean of men who do not). What is the p-value of the test? What is your conclusion? (Don't forget to state your hypotheses!)

1. Based on the 95% confidence interval, would you have expected to reject or not reject the null hypothesis. Why?

1. (8 points) (Pagano/Gauvreau Ch 10 Q 16) Two infant development indices - the Psychomotor Development Index (PDI) and Mental Development Index (MDI) - are used to assess a child's level of functioning in each of these areas at approximately one year of age. Among healthy infants, both indices have a mean value of 100. As part of a study, the scales were administered to infants born with congenital heart disease. The data are in the data setheart.dta.

1. At the 0.05 significance level, test the null hypothesis that the mean PDI scores for children born with congenital heart disease is equal to 100, the mean score for healthy children. Use a two-sided test. What is the p-value? What do you conclude? (Don't forget to state your hypotheses!)

1. Conduct the analogous test for the MDI score. What do you conclude?

1. Construct 95% confidence intervals for the true mean PDI scores and the true mean MDI score for the population of children with congenital heart disease. Does either of these intervals contain the value 100? Would you have expected that they would?