Question

Yvon Hopps ran an experiment to determine the optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver​ high-quality popcorn with less than 9​% of the kernels left​ un-popped, on average. After experimenting with several​ bags, he determined that power 9 at 4 minutes was the best combination. To be sure that the method was​ successful, he popped 8 more bags of popcorn​ (selected at​ random) at this setting. All were of high​ quality, with the following percentages of uncooked​ popcorn: 4.1​, 10.6​, 8.4​, 8.6​, 7.7​, 5.9​, 2.9​, 2.4. Does the 95​% confidence interval suggest that he met his goal of an average of no more than 9​% uncooked​ kernels? Explain.

The 95​% confidence interval for the true mean percentage of unpopped kernels is (__ %, __%).

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	2.974054472
Sample Mean	6.325
Sample Size	8
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	1.051487042
Degrees of Freedom	7
t Value	2.3646
Interval Half Width	2.4864
Confidence Interval
Interval Lower Limit	3.84
Interval Upper Limit	8.81

The 95​% confidence interval for the true mean percentage of unpopped kernels is 3.84% ,8.81% .

he 95​% confidence interval suggest that he met his goal of an average of no more than 9​% uncooked​ kernels becasue confidence interval contain numbr less than 9