1. (06.02 LC) Which of the following terms describes when the null hypothesis is

Question

1. (06.02 LC) Which of the following terms describes when the null hypothesis is rejected when it should NOT be rejected? (2 points)

1) Significance level,

2)Type I error

3)Type II error

4)p-Value

5)Alternative hypothesis

2. (06.01 LC) A hypothesis test is conducted with a significance level of 5%. The alternative hypothesis states that more than 12% of a population is left-handed.The p-value for the test is calculated to be 0.23. Which of the following statements is correct?

1. We can conclude that more than 12% of the population is left-handed.

2.We cannot conclude that more than 12% of the population is left-handed.

3.We can conclude that more than 23% of the population is left-handed.

4.We can conclude that exactly 23% of the population is left-handed.

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

3. (06.02 MC) Which of the following increases the power of a significance test? (2 points) I. Decrease the variability of the data II. Decrease the p-value III. Increase

1. I only

2. II only

3. III only

4.I and III only

5. I, II, and III

4. (06.02 MC) 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?

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

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

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

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

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

5. (06.02 HC) Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0.98; Ha: p > 0.98; = 0.05). The test results in a p-value of 0.15. However, the company is unaware that it is actually producing 99% high-quality candy. What MOST likely happens as a result of the testing?

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

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

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

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

5. The company rejects H0 correctly.

6. (06.02 MC) 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) (10 points)

7. (06.01 MC) 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. (10 points)

Explanation / Answer

Solution:

   1) Which of the following terms describes when the null hypothesis is rejected when it should NOT be rejected?

" We reject H0 , when it is true " , it is the Type I error.

Thus term Type I error describes when the null hypothesis is rejected when it should NOT be rejected.

   2) A hypothesis test is conducted with a significance level of 5%. The alternative hypothesis states that more than 12% of a population is left-handed.The p-value for the test is calculated to be 0.23. Which of the following statements is correct?

Question says alternative hypothesis states that more than 12% of a population is left-handed.

Thus H0: p =0.12   Vs H1 : p > 0.12

Since p value = 0.23 > 0.05 level of significance , we fail to reject H0.

That is we accept H0.

Thus we can not conclude that more than 12% of the population is left-handed

3) Which of the following increases the power of a significance test?

I. Decrease the variability of the data II. Decrease the p-value III. Increase

Power = 1 - P( Type II Error)

If , increases , that is : P( Type I error ) Increases , then P( Type II Error) decreases and

hence Power increases.

If we increase p value , then chances of rejecting H0 becomes less , that is we accept H0 and hence it decreases Probability of Type I error and hence it decreases Power .

Thus increase of p value does not increase power.

Increasing of sample will decrease the variablity of data and more the sample size, more the power of the test.

hence options I. Decrease the variability of the data and III. Increase are correct.

Thus 4.I and III only is correct

4)

H0: Number of students who fail the course does not decrease
Vs
H1: There is decrease in Number of students who fail the course

What would happen if the school district makes a Type I error?

Type I error = Reject H0 , when H0 is true.

So here we claim that : the new technology software decreases the number of students who fail Algebra 1, when it does not decrease the number.

Thus correct option is 2. Claim the new technology software decreases the number of students who fail Algebra 1, when it does not decrease the number.

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