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Assignment for IHP525 Confidence Intervals
1. Weight of a newborn. A SRS is taken from a population of full-term newborns in a research. In this demographic, the standard deviation of birth weights is 2 pounds. Calculate the 95 percent confidence intervals for the following samples:
a) The number of people is 81, and the weight is 7.0 pounds.
b) n = 9 with a weight of 7.0 pounds
c) Which sample yields the most accurate mean birth weight estimate?
d) Apply what you learned in step a to the CI you calculated.
2. Confidence interval and P-value The P-value of a two-sided test of H0: = 0 is 0.03. Is there a chance that the 95 percent confidence interval for includes 0? Will 0 be included in the 99 percent confidence interval for? In each case, explain your reasoning.
3. The length of the menstrual cycle. The following are the menstrual cycle lengths (days) in an SRS of nine women: 31, 28, 26, 24, 29, 33, 25, 26, 28. Using a one-sample t-test, see if the mean menstrual cycle length differs substantially from a lunar month. (There are 29.5 days in a lunar month.) Assume that the population’s values follow a Normal distribution. Consider a two-sided option. Show all steps in the hypothesis-testing process.
4. The length of the menstrual cycle. The mean length of menstrual periods in an SRS of 9 women was estimated in Problem 3. Days with a standard deviation of 2.906 days were discovered in the data.
a) For the mean menstrual cycle length, calculate a 95% confidence interval.
b) Is the mean menstrual cycle duration substantially different from 28.5 days at 0.05 (two sided) based on the confidence interval you just calculated? Is it statistically significant when compared to = 30 days at the same-level? Give an explanation for your decision. (The relationship between confidence intervals and significance tests was discussed in Section 10.4 of your text.) Here, too, the same rules apply.)
Fluoridation of drinking water is a good example of this. The number of cavity-free children per 100 in 16 North American cities BEFORE and AFTER municipal water fluoridation schemes was investigated in a study. The data is listed in the table below. To utilize StatCrunch to calculate the needed information, you’ll have to manually type the data in.
a) For each city, calculate the delta values (After Before). Then plot the differences in a stemplot or boxplot. Interpret the plot of your story.
b) What percentage of cities saw an increase in the number of people without cavities?
c) Estimate the mean change with a 95% confidence interval (i.e. compute a 95 percent CI for the mean difference).
B. B. Gerstman, B. B. Gerstman, B. B. Gerstman, B. B. Gerstman (2015). Basic biostatistics: A guide to using statistics in public health (2nd ed.). Jones and Bartlett, Burlington, MA. 978-1-284-03601-5 is the ISBN number for this book.