A company needs to determine the optimum power and time settings for their new licorice-flavored popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 10% of the kernels left unpopped, on average - a value that thier market reserch says is demanded by their customers. Their research department experiments with several settings and determines that power 9 at 4 minutes is optimum. Their tests confirm that this setting meets the less than 10% requirement. They change the instrutions on the box and promote a new money back guarantee of less than 10% unpopped kernels.
a) If, in fact, the setting results in more than 10%, kernels unpopped, what kind of error have they made? What will the consequence be for the company?
What are the null and alternative hypotheses in this case?
A. H0:? > 10 vs HA:? = 10
B. H0:? = 10 vs HA:? <10
C. H0:? = 10 vs HA:? >10
D. H0:? < 10 vs HA:? =10
a-1) If the setting results in more than 10% kernels unpopped, what kind of error have they made? What will the consequence be for the company?
A. They have made a Type 1 error. Customers will be disappointed to find less than 10% unpopped kernels. They may demand their money back.
B. They have made a Type 1 error. Customers will be disappointed to find more than 10% unpopped kernels. They may demand their mondy back.
C. They have made a Type 2 error. Customers will be disappointed to find more than 10% unpopped kernels. They may demand their money back.
D. They have made a Type 2 error. Customers will be disappointed to find less than 10% unpopped kernels. They may demand their money back.
b) To be sure that the method was successful, the research department popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the percentage of unpopped kernels shown below.
10.1, 4.6, 6.7, 9.5, 9.6, 6.4, 11.6, 3.2
Does this provide evidence that they met their goal of an average of fewer than 10% unpopped kernels? Assume ?= 0.05
what is the value of the test statistic?
What is the P-value of the test statistic?
Does this provide evidence that they met their goal of an average of fewer than 10% unpopped kernels? Assume ? = 0.05. Choose the correct answer below.
Yes/ No, there is/ is not enough evidence to conclude that more than/ less than/ exactly 10% of the kernels were left unpopped. The company should fail to reject/ reject the null hypothesis.