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.

  

Summary	Count	Mean	Median	MidRange	StdDev	Range	IntQRange
tempeture	43	98.457	98.000	98.600	0.8847	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.

A. The 90?% confidence interval would be wider because wider intervals are more likely to contain a population parameter.

B. The 90?% confidence interval would be narrower because wider intervals are less likely to contain a population parameter.

C. The 90?% confidence interval would be wider because wider intervals are less likely to contain a population parameter.

D. The 90?% confidence interval would be narrower because wider intervals are more likely to contain a population parameter.

b) What are the advantages and disadvantages of the 98?% confidence? interval?

A. 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.

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?) than the 90?% confidence interval. Your answer is correct.

C. 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.

D. 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. ?

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.

A. The confidence interval would likely be wider because a larger sample would cause the standard error to be smaller.

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 larger.

D. The confidence interval would likely be narrower 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 0.2 degrees with 98?% ?confidence?

Round up to the nearest whole? number.)

Answer 1

a)Option D. 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?) than 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.

[Large sample will imply small standard error which will imply small margin of error which will finally imply that the interval will be narrower.]

d) Margin of error = 0.2
=> (s/?n). t _{0.02/2; n-1} = 0.2
=> (0.8847/?n). t _{0.01; n-1} = 0.2
=> (t _{0.01; n-1}/?n) = 0.2/0.8847 = 0.2261
=> n = 109 (Found by trial and error)