Katie Sr Yr stats final practice set 4 (problem 11)

Problem 1: Stapler Lifespan A company claims that their heavy-duty stapler lasts 25,000 staples before breaking. A sample of 40 staplers is tested and has an average lifespan of 23,800 staples. The population standard deviation is known to be 2,200 staples. Test the company’s claim at a 0.05 significance level. What are the null and alternative hypotheses?

• H0:μ=25,000,H1:μ>25,000

• H0:μ=25,000,H1:μ≠25,000

• H0:μ>25,000,H1:μ=25,000

• H0:μ=23,800,H1:μ=25,000

Problem 2: Type of Test - What type of test should be used?

• 2-sample t-test

• 1-sample z-test

• 1-proportion z-test

• 1-sample t-test

Problem 3: Test Statistic - What is the test statistic?

• -3.45

• -2.87

• -1.75

• -4.11

Problem 4: P-value - What is the P-value?

• 0.00056

• 0.0052

• 0.0001

• 0.018

Problem 5: Decision-What is the appropriate decision at α = 0.05?

• Fail to reject the null hypothesis

• Retest with a larger sample size

• Reject the null hypothesis

• Lower the significance level

Problem 6: Conclusion-What conclusion can be made?

• There is strong evidence that the average lifespan is different from 25,000 staples.

• There is strong evidence that the staplers last more than 25,000 staples.

• There is no evidence that the staplers fail prematurely.

• The sample was biased.

Problem 7: Yogurt Cup Fill Volume A yogurt company claims that each cup contains exactly 150 grams of yogurt. A quality control team inspects 50 cups and finds the average content is 147.8 grams. The population standard deviation is known to be 3.6 grams. Test the company’s claim at the 0.05 significance level. Hypotheses - What are the null and alternative hypotheses?

• H0:μ=150,H1:μ≠150

• H0:μ=147.8,H1:μ>147.8

• H0:μ>150,H1:μ 150

Problem 8: Type of Test - What type of test should be used?

• Chi-square test for standard deviation

• 1-sample t-test

• 2-sample z-test

• 1-sample z-test

Problem 9: Test Statistic - What is the test statistic?

• -4.31

• -3.07

• -2.54

• -1.93

Problem 10: P-value- What is the P-value?

• 1.62×10−5

• 0.002

• 9.84×10−4

• 0.015