Question

1. A hypothesis test is conducted with a significance level of 5%. The alternative hypothesis states that more than 65% of a population is right-handed. The p-value for the test is calculated to be 0.03. Which of the following statements is correct?

A .We can conclude that more than 3% of the population is right-handed.

B .We cannot conclude that more than 65% of the population is right-handed.

C .We can conclude that more than 65% of the population is right-handed.

D .We can conclude that exactly 3% of the population is right-handed.

E .There is not enough information given to make a conclusion.

2. A manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease. One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

3. A food distributor is being sued for racial discrimination because 12% of newly hired candidates are not white when 53% of all applicants were not white. You plan to use hypothesis testing to determine whether there is significant evidence that the company's hiring practices are discriminatory.

Part A: State the null and alternative hypotheses for the significance test. (2 points)

Part B: In the context of the problem, what would a Type I error be? A Type II error? (2 points)

Part C: If the hypothesis is tested at a 1% level of significance instead of 5%, how will this affect the power of the test? (3 points)

Part D: If the hypothesis is tested based on the hiring of 1,000 employees rather than 100 employees, how will this affect the power of the test? (3 points)

Answer 1

Ans:

1)

Given that

p-value=0.03

signficance level=0.05

As,p-value<0.05,we reject the null hypothesis.

Option C is correct.

We can conclude that more than 65% of the population is right-handed.

2)

Sample proportion=135/175=0.7714

Test statistic:

z=(0.7714-0.85)/SQRT(0.85*(1-0.85)/175)

z=-2.91

p-value=P(z<-2.91)=0.0018

As,p-value<0.05,we reject the null hypothesis.

There is sufficient statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making