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IHP 525 Module Six Problem Set

1. Hemoglobin levels in 11-year-old boys vary according to a normal distribution with σ=1.2 g/dL.

a) How large a sample is needed to estimate µ with 95% confidence so the margin of error is no greater than 0.5 g/dL?

2. A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The test was carried out with a power of 85%. Assuming that this study was well designed and carried out properly, do you believe that there really is no significant difference in blood pressure? Explain your answer.

3. Would you use a one-sample, paired-sample, or independent-sample t-test in the following situations?

a) A lab technician obtains a specimen of known concentration from a reference lab. He/she tests the specimen 10 times using an assay kit and compares the calculated mean to that of the known standard.

b) A different technician compares the concentration of 10 specimens using 2 different assay kits. Ten measurements (1 on each specimen) are taken with each kit. Results are then compared.

4. In a study of maternal cigarette smoking and bone density in newborns, 77 infants of mothers who smoked had a mean bone mineral content of 0.098 g/cm3 (s1 = 0.026 g/cm3). The 161 infants whose mothers did not smoke had a mean bone mineral content of 0.095 g/cm3 (s2 = 0.025 g/cm3).

a) Calculate the 95% confidence interval for µ1 – µ2.

b) Based on the confidence interval you just calculated, is there a statistically significant difference in bone mineral content between newborns with mothers who did smoke and newborns with mothers who did not smoke?

5. A randomized, double-blind, placebo-controlled study evaluated the effect of the herbal remedy Echinacea purpurea in treating upper respiratory tract infections in 2- to 11-year olds. Each time a child had an upper respiratory tract infection, treatment with either echinacea or a placebo was given for the duration of the illness. One of the outcomes studied was “severity of symptoms.” A severity scale based on four symptoms was monitored and recorded by the parents of subjects for each instance of upper respiratory infection. The peak severity of symptoms in the 337 cases treated with echinacea had a mean score of 6.0 (standard deviation 2.3). The peak severity of symptoms in the placebo group (np = 370) had a mean score of 6.1 (standard deviation 2.4). Test the mean difference for significance using an independent t-test. Discuss your findings.

IHP 525 Quiz Two

1. A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time.

a. True or False: Each call is an independent random event.

In two attempts, what is the probability of achieving……

b. exactly two successful calls? (success = reach a live person)

c. one success and one failure (in any order)?

2. The prevalence of a trait is 76.8%. In a simple random sample of n = 50, how many individuals are expected to exhibit this characteristic and what is the corresponding standard deviation of this estimate?

3. Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with Salmonella. If Salmonella contamination occurs independently within and between egg cartons and Linda makes a three egg omelet, what is the probability that her omelet will contain at least one Salmonella contaminated egg?

4. Suppose that heights of 10-year old boys vary according to a Normal distribution with µ = 138 cm and σ = 7 cm. What proportion of 10-year old boys is less than 140 cm in height?

5. A survey selects a simple random sample of n = 500 people from a town of 55,000. The sample shows a mean of 2.3 health problems per person. Based on this information, say whether each of the following statements is true or false. Explain your reasoning in each instance. No calculations necessary.

a. It is reasonable to assume that the number of health problems per person will vary according to a normal distribution.

b. It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution.

6. A simple random sample of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately normally distributed with σ = 2.8 inches. Conduct a two-sided hypothesis test to determine whether the male students have heights that are significantly different than expected. Show all hypothesis testing steps.

7. True or false? The p-value refers to the probability of getting the observed result or something more extreme assuming the null hypothesis.