we found the following summary statistics for the Fahrenheit temperature of male
ID: 2931066 • Letter: W
Question
we found the following summary statistics for the Fahrenheit temperature of males Sample size: 65 Sample mean: 98.1 degrees Fahrenheit Sample Standard deviation: 0.70 In this investigation, you will investigate what happens to confidence intervals and hypothesis tests as we alter the level of confidence or change the sample size. Use the above summary statistics for the investigation and assume that the mean and the sample standard deviation do not change a. If you leave the sample size alone but increase your confidence level, what happens to the width of the confidence interval? Be as specific as possible and provide a rationale If you leave the confidence level alone (at 95%), what happens to the width of a confidence interval if you double the sample size? What if you triple it? What if you quadruple it? Be specific and provide a rationale If you are performing a hypothesis test, what is analogous to increasing your confidence level? What is different about conducting the hypothesis test as you make this change? Be as specific as possible and provide a rationale What happens to the p-value of the hypothesis test when you double the sample size? What if you quadruple it? Be as specific as possible and provide a rationale b. c. d.Explanation / Answer
Ans:
n=65>30,so central limit theorm is applicable(we will assume normal distribution)
a)As we increase the confidence level,multiplier z increases,so it increase margin of error and hence width of the confidence interval.
say 95% Confidence interval:
=98.1+/-1.96*(0.7/sqrt(65))
=98.1+/-0.17
=(97.93,98.27)
CI width=0.34
if 99% CI
=98.1+/-2.58*(0.7/sqrt(65))
=98.1+/-0.22
=(97.88,98.32)
CI width=0.44
b)n=130(doubled)
95% Confidence interval:
=98.1+/-1.96*(0.7/sqrt(130))
=98.1+/-0.12
=(97.98,98.22)
CI width=0.24
For,n=65*3=195
CI width=0.2
For,n=65*4=260
CI width=0.18
As,we increase the sample size,margin of error decreases,so width of CI decreases.
c)If we increase the confidence level,it will increase the critical z value or rejection region decreases,we are less likely to reject null hypothesis.
say confidence level=0.95,so significance leve=1-0.95=0.05
if p-value<0.05,we reject null hypothesis.
Now, confidence level=0.99,so significance leve=1-0.99=0.01
if p-value<0.01,we reject null hypothesis.(here we are less likely to reject null hypothesis as 0.01 is smaller than 0.05)
d)when we double the sample size,z statistic will increase and p-value will decrease.
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