Katie Sr Yr stats practice set 3 (problem 10)

Problem 1: Coffee Temperature A barista claims that their coffee is served hotter than the industry standard of 160°F. A health inspector randomly samples 25 cups and finds an average temperature of 165.2°F with a sample standard deviation of 4.5°F. Test the barista’s claim at the 0.05 significance level. Part 1: Hypotheses - What are the null and alternative hypotheses?

• H0:μ=160,H1:μ>160

• H0:μ=160,H1:μ≠160

• H0:μ=165.2,H1:μ160,H1:μ=160

Problem 2: Test Statistic What is the value of the test statistic?

• 4.23

• 5.78

• 3.15

• 2.61

Problem 3: What is the P-value?

• 1.025×10−6

• 6.018×10−7

• 2.51×10−5

• 4.32×10−4

Problem 4: Decision - What is the appropriate decision?

• Fail to reject H0

• Increase the significance level

• Reject H0

• Retest using a z-test

Problem 5: Conclusion What conclusion can be made?

• There is strong evidence that the coffee is hotter than 160°F

• There is not enough evidence to support the barista’s claim

• There is strong evidence that the coffee is cooler than 160°F

• The coffee temperature is exactly 165.2°F

Problem 6: Test Prep Class Effectiveness A test prep company claims their students score higher than the national average of 510 on the SAT Math section. A random sample of 40 students shows an average score of 527 with a standard deviation of 28 points. Test the company’s claim at the 0.05 significance level. Part 1: Hypotheses What are the null and alternative hypotheses?

• H0:μ=510,H1:μ510

• H0:μ>510,H1:μ=510

• H0:μ=527,H1:μ≠527

Problem 7: Test Statistic What is the value of the test statistic?

• 3.17

• 4.01

• 3.84

• 2.95

Problem 8: Question - What is the P-value?

• 3.72×10−4

• 7.01×10−5

• 1.27×10−3

• 9.94×10−5

Problem 9: Decision - What is the appropriate decision?

• Fail to reject H0

• Reject H0

• Retest with a different sample

• Increase the significance level

Problem 10: Conclusion - What conclusion can be made?

• There is strong evidence that the company improves math scores above 510

• There is not enough evidence to say the average score is different

• The prep class has no measurable effect

• SAT Math scores follow a normal distribution