Katie Sr Yr Stats Final part 5 (problem 12)

Problem 1: Reaction Time Variability A psychology researcher believes that the standard deviation of student reaction times is greater than 0.6 seconds. A random sample of 8 students produced the following reaction times (in seconds): 0.42, 0.55, 0.67, 0.80, 0.52, 0.71, 0.63, 0.77 Test the researcher’s claim at the 0.05 significance level. Assume reaction times are normally distributed. Hypotheses - What are the null and alternative hypotheses?

• H0:σ=0.6,H1:σ>0.6

• H0:μ=0.6,H1:μ≠0.6

• H0:σ=0.6,H1:σ≠0.6

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

• Chi-square test for variance

• 1-sample z-test

• 2-proportion z-test

• 1-sample t-test

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

• 0.33

• 1.12

• 2.29

• 3.07

Problem 4: Critical Value - What is the critical value?

• 12.254

• 13.362

• 14.067

• 15.507

Problem 5: Decision - What is the appropriate decision?

• Reject H0

• Fail to reject H0

• Use a t-test instead

• Increase the sample size

Problem 6: Conclusion - What conclusion can be made?

• There is not enough evidence that the standard deviation is greater than 0.6 seconds.

• There is strong evidence that the standard deviation is greater than 0.6 seconds.

• There is not enough evidence that the average time is different from 0.6 seconds.

• There is strong evidence that the average time is greater than 0.6 seconds.

Problem 7: Blood Pressure Device Precision A biomedical engineer wants to verify if a new blood pressure device has a standard deviation in readings less than 5 mmHg. A random sample of 10 readings yields the following values: 120, 116, 123, 117, 119, 115, 121, 118, 122, 116 Test the claim that the standard deviation is less than 5 mmHg, using a 0.01 significance level. Assume normality. Hypotheses - What are the null and alternative hypotheses?

• H0:σ=5,H1:σ>5

• H0:σ=5,H1:σ<5

• H0:σ=5,H1:σ≠5

• H0:μ=5,H1:μ<5

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

• Chi-square test for variance

• 1-sample t-test

• 2-sample F-test

• z-test for means

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

• 1.75

• 2.60

• 3.92

• 4.51

Problem 10: Critical Value - What is the critical value?

• 2.088

• 3.325

• 1.735

• 4.168