Question

Beth ran an experiment to test optimum power and time settings for microwave popcorn. Her goal was to deliver popcorn with fewer than 11% of the kernels left​ unpopped, on average. She determined that power 9 at 4 minutes was the best combination. To be sure that the method was​ successful, she

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.

10.1​, 3.2​, 8.6​, 6.2, 11.2, 2.7​, 12.6​, 10.7

  

Does this provide evidence that she met her goal of an average of fewer than 10% unpopped​ kernels? Use 0.05 as the​ P-value cutoff level.

Choose the correct null and alternative hypotheses.

A.

H0​: μ≠11

HA​: μ=11

B.

H0​: μ<11

HA​: μ=11

C.

H0​: μ=11

HA​: μ<11

D.

H0​: μ>11

HA​: μ=11

E.

H0​: μ=11

HA​: μ≠11

F.

H0​: μ=11

HA​: μ>11

Calculate the test statistic.

t=

​(Round to three decimal places as​ needed.)

Calculate the​ P-value.

​P-value =

​(Round to four decimal places as​ needed.)

Does this provide evidence that Beth met her goal?

A.

Yes​, there is enough evidence to suggest that less than 11​% of the kernels are left unpopped when the specified power and time settings are used.

B.

​No, there is not enough evidence to suggest that at least 11​% of the kernels are left unpopped when the specified power and time settings are used.

C.

No​, there is not enough evidence suggest that less than 11​% of the kernels are left unpopped when the specified power and time settings are used.

D.

​Yes, there is enough evidence to suggest that at least 11​% of the kernels are left unpopped when the specified power and time settings are used.

Answer 1

Yes​, there is enough evidence to suggest that less than 11​% of the kernels are left unpopped when the specified power and time settings are used.