Question

Bernard ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to deliver popcorn with fewer than 12​%

of the kernels left ​unpopped, on average. 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 percentages of unpopped kernels shown below.

7.87.8​, 5.85.8​, 12.612.6​, 8.78.7​,10.510.5​, 9.29.2​, 2.92.9​, 8.58.5

Does this provide evidence that he met his goal of an average of fewer than 12​% unpopped​ kernels? Use 0.05 as the​ P-value cutoff level.

Calculate the test statistic

t=

Answer 1

From the given sample data : Sample size=n=8 , ,

Therefore , Sample mean=

Sample standard deviation=s=

Also given that , Significance level=

Hypothesized value=

Hypothesis : Vs  

The test statistic is ,

The p-value is ,

p-value= ; From excel "=TDIST(3.6235,7,1)"

Decision : Here , p-value=0.0042<

Therefore , Reject the null hypothesis.

Conclusion : Hence , the data provide the sufficient evidence that he met his goal of an average of fewer than 12​% unpopped​ kernels.