Hypothesis Testing with Two Samples

• Explain how the test statistic relates to the critical value in a hypothesis test.

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• Is it possible to reach different decisions about the null hypothesis when switching from the critical value method to the P-value method? Explain your reasoning
• Determine if the following represents an example of an independent or dependent data set. Pain levels in a group of 30 patients are measured before administering a new headache medicine, and then pain levels are measured again 1 hour after administering the medicine.

Use the information described in Question 4 to answer questions 4 through 9. Note that the parameters given in Question 4 are subject to randomization and may result in different numeric results on subsequent attempts.

All calculations must be accurate to the nearest thousandth place and include any leading zeros.

Use the following scenario for questions to conduct a hypothesis test. In a random sample of 500 people aged 20-29, 14% were smokers. In a random sample of 450 people aged 30-99, 18% were smokers. Test the claim that the proportion of smokers in the two age groups is the same. Use a significance level of 0.01.

• Write the symbolic form of the null and alternative hypothesis. Indicate the direction of the test.
• Calculate the test statistic.
• Describe the formula used for the test statistic, and identify what each variable represents.
• Calculate the P-value.
• Describe how the P-value was calculated.
• Make a decision about the null hypothesis. Use this decision to make a conclusion about the claim.

Use the information described in Question 10 to answer questions 10 through 15. Note that the parameters given in Question 10 are subject to randomization and may result in different numeric results on subsequent attempts.

All calculations must be accurate to the nearest thousandth place and include any leading zeros.

Use the following scenario to conduct a hypothesis test. A study is done to determine if public sector employees retire at a younger age than private sector employees. A random sample of 150 public sector employees was found to have an average retirement age of 64.1 years old with a standard deviation of 2.73. A random sample of 210 private sector employees was found to have an average retirement age of 64.7 years old with a standard deviation of 1.91. Test the claim that public sector employees have a lower average retirement age than private sector employees at a 0.01 level of significance.

• Write the symbolic form of the null and alternative hypothesis. Indicate the direction of the test.
• Calculate the test statistic.
• Describe the formula used for the test statistic, and identify what each variable represents.
• Calculate the critical value.
• Describe how the critical value was calculated.
• Make a decision about the null hypothesis. Use this decision to make a conclusion about the claim