MAGDALENA LUCA



REVIEW PROBLEMS

I. Descriptive Statistics

1. What measures of central tendency and dispersion are the most appropriate to use with the following sets of data?

a. Salaries of 125 physicians in a clinic.

b. The test scores of all medical students taking the National Board Examination in a given year.

c. Serum sodium levels of healthy individuals.

d. The age at onset of breast cancer in females.

e. The number of pills left in subjects’ medicine bottles when investigators in a study counted the pills to evaluate compliance in taking medication.

2. Refer to Figure 3-2 below to answer the following questions:

a. What is the mean weight of girls 24 months old?

b. What is the 90th percentile for head circumference for 12-month-old girls?

c. What is the fifth percentile in weight for 12-month-old girls?

[pic]

II. DISTRIBUTIONS

1. Find the 75th percentile of the standard normal distribution.

2. Find the 25th percentile of the standard normal distribution.

3. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a. Find the probability of a pregnancy lasting 308 days or longer.

b. If we stipulate that a baby is premature if the length of pregnancy is in the lowest 4%, find the length of a pregnancy that separates premature babies from those who are not premature. This result could be helpful to hospital administrators in planning for that care.

4. Birth weights in the United States are normally distributed with a mean of 3420 g and a standard deviation of 495 g. If a hospital plans to set up special observation conditions for the lightest 2% of babies, what weight is used for the cutoff separating the lightest 2% from the others?

5. A data set includes a sample of 106 body temperatures of adults. If we construct a histogram to depict the shape of the distribution of that sample, does that histogram show the shape of a sampling distribution of sample means? Why or why not?

6. Given the information in the following table, answer the following questions (using the Empirical Rule):

a. Assuming that the distribution of self-reported height for men is normal, the middle 95% of men reported heights between what two values?

b. Assuming that the distribution of age is normal, approximately what percentage of students was more than 17 year old?

c. Assuming that the distribution of measured weight for women is normal, the middle 68% of women had weights between what two values?

d. Assuming that the distribution of age is normal, approximately what percentage of students was between 14.1 and 25.7 years old?

e. Assuming that the distribution of self-reported weight for women is normal, approximately what percentage of women reported weights above 43.08kg?

f. Assuming that the distribution of measured height for men is normal, what is the 84th percentile?

|Comparison of Self-Reported and Measured |

|Height and Weight for Men (n=30) and Women (n=32) |

| |[pic] |SD |

HEIGHT |Men |Self-Reported height (in m) |1.79 |0.07 | | | |Measured height (in m) |1.78 |0.06 | | |Women |Self-Reported height (in m) |1.62 |0.07 | | | |Measured height (in m) |1.62 |0.07 | |

WEIGHT |Men |Self-Reported weight (in kg) |79.70 |13.39 | | | |Measured weight (in kg) |79.20 |14.44 | | |Women |Self-Reported weight (in kg) |61.20 |9.06 | | | |Measured weight (in kg) |63.10 |10.02 | |

III. CONFIDENCE INTERVALS

1. A zoologist measured the tail length in 86 individuals, all in the 1-year age group, of the deer mouse Peromyscus. The mean length was 60.43 mm and the standard deviation was 3.06 mm.

A. Suppose the zoologist were to measure 500 additional animals from the same population.

a. What would you predict would be the standard deviation of the 500 new measurements?

b. What would you predict would be the standard error of the mean for the 500 new measurements?

B. A 95% confidence interval for the mean is [pic].

a. True or false: We are 95% confident that the average tail length of the 86 individuals in the sample is between 59.77 mm and 61.09 mm.

b. True or false: We are 95% confident that the average tail length of all individuals in the population is between 59.77 mm and 61.09 mm.

2. A group of 101 patients with end-stage renal disease were given the drug epoetin. The mean hemoglobin level of the patients was 10.3 g/dL, with a SD of 0.9 g/dL. Construct a 99% confidence interval for the population mean and interpret it.

3. As part of a study of natural variation in blood chemistry, serum potassium concentrations were measured in 61 healthy women. The mean concentration was 4.36mEq/L, and the standard deviation was 0.42mEq/L.

a. Construct a 95% CI for the population mean and interpret it.

b. Calculate the margin error associated with a 95% CI.

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