To find out what proportion of dogs are given heartworm medication, we survey 50

Question

To find out what proportion of dogs are given heartworm medication, we survey 50 dog owners by telephone each night for a period of 20 nights. From the data collected, twenty different sample proportions and 95 percent confidence intervals (one for each night's sample) were computed.

a) Do all 20 of the confidence intervals have the same length?

b) Suppose you calculated 90% confidence intervals instead of 95% confidence intervals. Would they be narrower or wider?

c) Suppose you surveyed 100 dog owners by telephone each night instead of 50. Would the width of the 90% confidence intervals constructed using n=100 be narrower or wider than the 90% confidence intervals constructed using n=50 ?

d) What about 99% confidence intervals - for the same sample size, would they be narrower or wider than 95% confidence intervals ?

Explanation / Answer

a) Do all 20 of the confidence intervals have the same length?

No, because the length of the confidence interval depends on margin of error and margin of error depends on sample standard deviation and sample size. Since sample standard deviation of each sample would be different, all 20 of the confidence intervals will not have the same length.

--------------------------------------------------------------------------------------------------------------------------

b) Suppose you calculated 90% confidence intervals instead of 95% confidence intervals. Would they be narrower or wider?

Narrower: The 90% confidence interval would be narrower (smaller margin of error) than the 95% confidence interval, because it allows one to be less confident that the unknown population parameter is contained within the interval.

--------------------------------------------------------------------------------------------------------------------------

c) Suppose you surveyed 100 dog owners by telephone each night instead of 50. Would the width of the 90% confidence intervals constructed using n=100 be narrower or wider than the 90% confidence intervals constructed using n=50 ?

Narrower: As sample size increases, margin of error decreases. Therefore, width of the 90% confidence intervals constructed will also decrease.

--------------------------------------------------------------------------------------------------------------------------

d) What about 99% confidence intervals - for the same sample size, would they be narrower or wider than 95% confidence intervals ?

Wider: The 99% confidence interval would be wider (larger margin of error) than the 95% confidence interval, because it allows one to be more confident that the unknown population parameter is contained within the interval.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.