You take a random sample of 51 reduced-sugar cookies and test them in a lab. fin

Question

You take a random sample of 51 reduced-sugar cookies and test them in a lab. finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams of sugar. Create a 99% confidence interval for die mean grams of sugar. While performing a strenuous task, the pulse rate of 25 workers increased on the average by 18.4 beats per minute with a standard deviation of 4.9 beats per minute. A) Construct a 90% confidence interval for the population standard deviation of the increase in pulse rate when performing this task. B) Construct a 99% confidence interval for the population standard deviation of the increase in pulse rate when performing this task. C) Reflect on the confidence interval range if the confidence level increases. In a time use study 20 randomly selected managers were found to spend a mean time of 2.4 hours per day on paperwork. The standard deviation of the 20 scores was 1.30 hours. Construct a 98% confidence interval for the mean time spent on paperwork by all managers. In a random sample of 800 adults in the U.S.A., it was found that 72 of those had a pinworm infestation.

Explanation / Answer

1) here std error of mean =std deviation/(n)1/2 =0.154

for 50 degree of freedom and 99% CI. t=2.6778

hence confidence interval =sample mean -/+ t*Std error =2.7875 ; 3.6125

2)a) std error =0.98

for 90% CI and 24 degree of freedom ; t=1.7109

hence confidence interval =sample mean -/+ t*Std error =16.7233 ; 20.0767

b)

for 99% CI and 24 degree of freedom ; t=2.7969

hence confidence interval =sample mean -/+ t*Std error=15.6590 ; 21.1410

c) confidence interval range increases with confidence level

3)std error =0.2907

for 19 df and 98%,CI, t=2.5395

hence confidence interval =sample mean -/+ t*Std error=1.6618 ; 3.1382

please reply for doubt

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