Question

1) A psychologist claims that more than 62 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. There is sufficient evidence to support the claim that the true proportion is less than 62 percent. There is sufficient evidence to support the claim that the true proportion is greater than 62 percent. There is not sufficient evidence to support the claim that the true proportion is greater than 62 percent. There is not sufficient evidence to support the claim that the true proportion is less than 62 percent. — 2) A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below: Brand 1 2 3 4 5 Customers 55 30 18 65 32 Assume that we will test the claim that the distribution of preferences is uniform, using a significance level of a =0.01. Find the critical value for the test. 11.143 14.860 13.277 9.488

Answer 1

1)

Aim - To test the claim that more than 62 percent of population suffers from professional problems due to extreme shyness.

H0 : P = 0.62

H1 : P > 0.62

Here we have failure to to reject null hypothesis.

Ans.:- There is not sufficient evidence to support the claim that the true proportion is greater than 62 percent.

2)

Here total brand are 5

K = 5

$\alpha = 0.01$

Critical value of test = $\chi^{2}_{\alpha,k-1} = \chi^{2}_{0.01, 4} = 13.277$

Ans.:- 13.277