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.
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.
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