Question

The manager of a certain merchandising shop selling perfumes believes that his market share is 60%. A sample was used to test this hypothesis. However, you disagree, counterclaiming that: 1. The merchandiser's market share is actually not 60%. OR 2. The merchandiser's market share does not exceed 60%. OR 3. The merchandiser's market share is more than 60%.REQURED. a. Formulate the NULL Hypothesis for each of the three scenarios above(1,2 and 3). b. Formulate the alternative hypothesis or each of the three scenario above(1,2 and 3). c. Use sketch or diagram (for each) of the normal curve clearly indicating the regions(s) of acceptance and rejection. d. If you were given that all the tests were performed at 1% level of significance determine the critical value for each of the scenarios (1,2 and 3). e. If 300 out of the selected sample were found to favor the merchandiser's perfume, calculate the test statistics for the problem. f. State whether you would accept or reject the null hypothesis in each of the counter claims (1),(2) and (3).

Answer 1

Soln

a)

Scenario 1

Null Hypothesis

H₀: p = 0.6

Scenario 2

Null Hypothesis

H₀: p = 0.6

Scenario 3

Null Hypothesis

H₀: p = 0.6

b)

Scenario 1

Alternate Hypothesis

H_a: p <> 0.6

Scenario 2

Alternate Hypothesis

H_a: p < 0.6

Scenario 3

Alternate Hypothesis

H_a: p > 0.6

c)

Scenario 1

In the above diagram the Green Coloured Area is the region of acceptance and the rejection area are white and yellow

Scenario 2

In the above diagram the Green Coloured Area and Yellow Area are the region of acceptance and the rejection area is the white coloured

Scenario 3

In the above diagram the Green Coloured Area and White Area are the region of acceptance and the rejection area is the yellow coloured

d)

Scenario 1

Critical values are -2.33 and 2.33

Scenario 2

Critical value is -2.33

Scenario 3

Critical value is 2.33

e)

We cannot calculate the test statistic without the sample size

f)

We cannot accept or reject the hypothesis without the test statistic