A researcher measured the body temperatures of a randomly selected group of adul

Question

A researcher measured the body temperatures of a randomly selected group of adults. He wishes to estimate the average temperature among the adult population. Summaries of the data he collected are presented in the table below Complete parts (a) through (d) below Count 43 Median 98.400 MidRange 98.800 Std Dev 0.8388 Range 2.800 Summary Mean 98.204 1.050 a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval? Explain. Choose the correct answer below. A. The 90% confidence interval would be narrower because wider intervals are more likely to contain a population parameter The 90% confidence interval would be wider because wider intervals are less likely to contain a population parameter. O B. C. The 90% confidence interval would be narrower because wider intervals are less likely to contain a population parameter The 90% confidence interval would be wider because wider intervals are more likely to contain a population parameter D. b) What are the advantages and disadvantages of the 98% confidence interval? A wider than the 90% The 98% confidence interval has a lesser chance of containing the true mean body temperature of adults than the 90% confidence interval, but the 98% confidence interval is more precise confidence interval The 98% confidence interval has a greater chance o containing the true mean body temperature of adults than the 90% confidence interval but the 98% confidence interval is less precise confidence interval B wider than the 90% O O c) If further research is conducted, this time using a sample of 500 adults, how is the 98% confidence interval likely to change? Explain. Choose the correct answer below. The 98% confidence interval has a lesser chance o containing the rue mean body temperature o adults than the 9 % confidence interval but the 9 % con dence interval s more precise narrower than the 0% confidence interval The 98% confidence interval has a greater chance o containing he rue mean body temperature o adults than he 90% confidence interval but the 98% confidence interval is less precise narrower than the 90% confidence interval A. The confidence interval would likely be narrower because a larger sample would cause the standard error to be larger. O B. The confidence interval would likely be narrower because a larger sample would cause the standard error to be smaller. C. The confidence interval would likely be wider because a larger sample would cause the standard error to be smaller. O D. The confidence interval would likely be wider because a larger sample would cause the standard error to be larger.

Explanation / Answer

a) Option A: The 90% confidence interval would be narrower because wider intervals are more likely to contain a population parameter

b) Option B: The 98% confidence interval has a greater chance of containing the true mean body temperature of adults than the 90% confidence interval, but the 98% confidence interval is less precise(wider) that the 90% confidence interval

c) Option B: The confidence interval would likely be narrower because a larger sample would cause the standard error to be smaller

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