problem set w-6

1.       A pharmacist reads that a 95% confidence interval for the average price of a particular prescription drug is $30.50 to $35.50. Asked to explain the meaning of this, the pharmacist says “95% of all pharmacies sell the drug for between $30.50 and $35.50.” Is the pharmacist correct? Explain your response.

2.       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?

b)      How large a sample is needed to estimate µ with margin of error 0.5 g/dL with 99% confidence?

3.       A t-test calculates t_stat = 6.60. Assuming the study had more than just a few observations, you do not need a t table or software utility to draw a conclusion about the test. What is this conclusion, and why is a look-up table unnecessary?

4.       A researcher fails to find a significant different in mean blood pressure in 36 matched pairs. The standard deviation of the difference was 5 mmHg. What was the power of the test to find a mean difference of 2.5 mmHg at α = 0.05 (two-sided)?

5.       Would you use a one-sample, paired-sample, or independent-sample t procedure 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 are taken with each kit. Results are then compared.

6.       In a study of maternal cigarette smoking and bone density in newborns, 77 infants of mothers who smoked has a mean bone mineral content of 0.098 g/cm³ (s₁ = 0.026 g/cm³). The 161 infants whose mothers did not smoke has a mean bone mineral content of 0.095 g/cm³ (s₂ = 0.25 g/cm³).

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

b)      Based on the confidence interval you just calculated, would you reject or retain H₀: µ₁ - µ₂ = 0 at α=0.05?

7.       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 (n2 = 370) had a mean score of 6.1 (standard deviation 2.4). Test the mean difference for significance. Discuss your findings.