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Chapter 8: Q97SE (page 452)
Consider two events A and B, with ,,and
a.Are A and B mutually exclusive?
b.Are A and B independent?
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Suppose you want to estimate the difference between two population means correct to within 1.8 with a 95% confidence interval. If prior information suggests that the population variances are approximately equal to and you want to select independent random samples of equal size from the populations, how large should the sample sizes , and , be?
Consider the discrete probability distribution shown here.
x | 10 | 12 | 18 | 20 |
p | .2 | .3 | .1 | .4 |
a. Calculate and .
b. What is ?
c. Calculate .
d. What is the probability that xis in the interval ?
Refer to the Archives of Paediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children’s cough remedy, Exercise 2.31 (p. 86). Children who were ill with an upper respiratory tract infection and their parents participated in the study. Parents were instructed to give their sick child dosage of liquid “medicine” before bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM)—an over-the-counter cough medicine—while others were given a similar dose of honey. (Note: A third group gave their children no medicine.) Parents then rated their children’s cough symptoms, and the improvement in total cough symptoms score was determined for each child. The data (improvement scores) for the 35 children in the DM dosage group and the 35 in the honey dosage group are reproduced in the next table. Do you agree with the statement (extracted from the article), “Honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection”? Use the comparison of the two means methodology presented in this section to answer the question.
The data is given below:
Honey Dosage: |
DM Dosage: |
Solar energy generation along highways. Refer to the International Journal of Energy and Environmental Engineering (December 2013) study of solar energy generation along highways, Exercise 8.39 (p. 481). Recall that the researchers compared the mean monthly amount of solar energy generated by east-west– and north-south– oriented solar panels using a matched-pairs experiment. However, a small sample of only five months was used for the analysis. How many more months would need to be selected to estimate the difference in means to within 25 kilowatt-hours with a 90% confidence interval? Use the information provided in the SOLAR file to find an estimate of the standard error required to carry out the calculation
Question: Independent random samples from approximately normal populations produced the results shown below.
Sample 1 | Sample 2 |
a. Do the data provide sufficient evidence to conclude that ? Test using.
b. Construct a confidence interval for . Interpret your result.
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