# . Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making?

Advanced Statistics – 5 questions (Proportions)

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Question 1:

A hypothesis test is conducted with a significance level of 10%. The alternative hypothesis states that more than 15% of a population has at least one sibling. The p-value for the test is calculated to be 0.27. Which statement is correct?

a. We can conclude that more than 27% of the population has at least one sibling.

b. We can conclude that exactly 27% of the population has at least one sibling.

c. We can conclude that more than 15% of the population has at least one sibling.

d. We cannot conclude that more than 15% of the population has at least one sibling.

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

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Order Paper NowQuestion 2:

Big Sweets candy company is testing one of its machines in the factory to make sure it is producing more than 96% high-quality candy (H0: p = 0.96; Ha: p > 0.96; α = 0.05). The test results in a p-value of 0.12. However, the company is unaware that it is actually producing 98% high-quality candy. What MOST likely happens as a result of the testing?

a. The company rejects H0, making a Type I error.

b. The company fails to reject H0, making a Type I error.

c. The company rejects H0, making a Type II error.

d. The company fails to reject H0, making a Type II error.

e. The company rejects H0 correctly.

Question 3:

A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error?

a. Claim the new technology software decreases the number of students who fail Algebra 1, when it does decrease the number.

b. Claim the new technology software decreases the number of students who fail Algebra 1, when it does not decrease the number.

c. Claim the new technology software does not decrease the number of students who fail Algebra 1, when it does decrease the number.

d. Claim the new technology software does not decrease the number of students who fail Algebra 1, when it does not decrease the number.

e. Claim the new technology software increases the number of students who fail Algebra 1, when it decreases the number.

Question 4:

A large restaurant is being sued for age discrimination because 15% of newly hired candidates are between the ages of 30 years and 50 years when 50% of all applicants were in that age bracket. 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)

Question 5:

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.