Question

1. The production manager of a company that produces an over-the-counter cold remedy wants to boost sales of the product. The product is considered effective by the people who have tried it, but many people decide not to buy it again because it tastes like day-old soapsuds. The manufacturer is trying to decide whether to add a lemon flavor to the product. Because the flavoring will increase production costs, the manager wants to be certain that people respond favorably to the flavoring before using it. Twenty people with colds are randomly sampled. On two difference occasions, each person uses the product and indicates which version (taste) is preferred. (They must pick one.)

1. State the competing hypotheses and the rejection region for α = .01.
2. What conclusion should be made if 16 people prefer the lemon-flavored product? What if 2 people prefer the lemon flavor?
3. Why would using α = .01 make sense in this case? If the results indicate that the null hypothesis should be rejected in favor of the alternative hypothesis, what additional problem(s) of interpretation might the production manager have to face?

Answer 1

The manager is testing whether by adding the lemon flavour has the probability of buying the remedy again increase or not. This is a test for population binomial proportion.

We will use a 1 -tailed z-test since the test is checking only in one direction (right tailed)

• state the competing hypotheses and the rejection region for α = .01.

Null Hypothesis: People's preference hasn't changed after adding the lemon flavour.

VS

Competing hypotheses : People's preference increase after adding the lemon flavour.

Rejection region at 0.01

= ..................Using normal distribution percentage tables or can be found online or in excel func 'normsinv'

• What conclusion should be made if 16 people prefer the lemon-flavored product? What if 2 people prefer the lemon flavor?

Since 20 people are sample then our n = 20 and 16 preferred therefore x = 16

Test Stat : ................................. Null proportion

=

= 3.3541

Criteria: To reject the null hypothesis if T.S> C.V.

Decision: Since Test stat > Critical Value

  We reject the null hypothesis at 1% level of significance. We also conclude that people significantly prefer lemon flavour.

If 2 people preferred in the experiment then x = 2

Test Stat:

= -5.962

Since |T.S|. > C.V.

We still reject the null hypothesis.

• Why would using α = .01 make sense in this case? If the results indicate that the null hypothesis should be rejected in favor of the alternative hypothesis, what additional problem(s) of interpretation might the production manager have to face?

The manager has to incur additional cost if he is adding lemon flavor. He has to be as sure as he can about his decision. So using a lower level of significance will provide him with a more strict (accurate ) answer. But we are rejecting the null hypo in both cases where 16 and 2 people preferred the flavor.  So using 0.01 is not making sense.

Additional problem that might occur is he makes a type 1 error, where he rejects the null hypothesis if it is true. That means he shouldn't have added the flavor and his incurring the additional cost would be in vain. The manager should also look at the power of the test which is the probability of rejecting the null hypothesis when it is false. The greater the power the greater the chance of accuracy of rejection.