Assignment:
Q1 A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean a of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two populations.
a. For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviation of X1-X2.
b. Can you conclude that the variable X1-X2 is normally distributed? Explain your answer.
c. Determine the percentage of all pairs of independent samples of sizes 9 and 4, respectively, from the two populations that have the property that the difference between the sample means is between -10 and 10.
Q2 The US National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital Health Statistics. Independent random samples of 39 males patients and 35 female patients gave the following data on length of stay, in days.
Male Female
4 4 12 18 9 4 7 15 1 12
6 12 10 3 6 1 3 7 21 4
15 7 3 13 1 1 5 4 4 3
2 10 13 5 7 5 18 12 5 1
1 23 9 2 1 7 7 2 15 4
17 2 24 11 14 9 10 7 3 6
6 2 1 8 1 5 9 6 2 14
3 19 3 1
a. At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the lengths of stay in short-term hospitals by males and females differ? Assume that O1=5.4 days and O2 4.6 days. (Note: The sum of the male data is 308 days, and the sum of the female data is 249 days.)
Q3 Offspring of Diabetic Mothers. Previous research indicates that children borne by diabetic mothers may suffer from obesity, high blood pressure, and glucose intolerance. Independent random samples of adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM) were taken by Cho et al. and evaluated for potential differences in vital measurements, including blood pressure and glucose tolerance. The study was published in The Journal of Pediatrics (Vol. 136(5), pp 587-592). The following summary statistics are for the systolic blood pressures, in mm Hg, of the 99 ODM and the 80 ONM participants.
ODM ONM
X1=118 X2=110
S1= 12.04 S2=11.25
N1=99 N2=80
At the 1% significance level, do the data provide sufficient evidence to conclude that the mean systolic blood pressure of ODM children exceeds that of ONM children?
Q4 Offspring of Diabetic Mothers. Refer to Exercise 10.24.
a. Determine a 98% confidence interval for the difference between the mean systolic blood pressures of ODM and ONM children. Note: You must use Z a/2 or T a/2 = 2.349 to determine the 98% confidence level.
b. Interpret your answer in part (a).
Q5 Nitrogen and Seagrass. The seagrass Thalassia testudinum is an integral part of the Texas coastal ecosystem. Essential to the growth of T. testudinum is ammonium. Researchers Kun-Seop Lee and Kenneth H. Dunton of the Marine Science Institute of the University of Texas at Austin noticed that the seagrass beds in Corpus Christi Bay (CBB) were taller and thicker than those in Lower Laguna Madre (LLM). They compared the sediment ammonium concentrations in two locations and published their findings in Marine Ecology Progress Series (Vol. 196, pp.39-48). Following are the summary statistics on sediment ammonium concentrations, in micromoles, obtained by the researchers.
CCB LLM
X1=115.1 X2=24.3
S1=79.4 S2=10.5
N1=51 N2=19
At the 1% significance level, is there sufficient evidence to conclude that the mean sediment ammonium concentration in CCB exceeds that in LLM?