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.
Summary Count Mean Median MidRange StdDev Range IntQRange Temperature 43 98.534 98.300 98.600 0.6664 2.800 1.050 a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval? Explain. Choose the correct answer below. O A. The 90% confidence interval would be narrower because wider intervals are more likely to contain a population parameter. O B. The 90% confidence interval would be wider because wider intervals are more likely to contain a population parameter. O C. The 90% confidence interval would be wider because wider intervals are less likely to contain a population parameter. O D. The 90% confidence interval would be narrower because wider intervals are less likely to contain a population parameter. b) What are the advantages and disadvantages of the 98% confidence interval? O A. 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 (wider) than the 90% confidence interval. O B. 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 (narrower) than the 90% confidence interval. O C. 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) than the 90% confidence interval. O D. 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 (narrower) than the 90% confidence interval. 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. O A. The confidence interval would likely be narrower because a larger sample would cause the standard error to be smaller. O B. The confidence interval would likely be narrower because a larger sample would cause the standard error to be larger. O 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. d) How large a sample would the researcher need to estimate the mean body temperature to within 0.1 degrees with 95% confidence? (Round up to the nearest whole number.)
