QI.[5 points]: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let µ = average age of onset for women and u2 = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, and assume the population variances are equal. i. What are the appropriate null and alternative hypothesis? ii. What is the value of the test statistics? iii. iv. Why you decided to use the test statistics in part ii ? For a significant level of 0.05, what is the critical value (or critical region)? What is the appropriate conclusion to this test? v.

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Q1.[5 points]: A researcher wants to assess if there is a difference in the average age of onset of a certain
disease for men and women who get the disease. Let µ = average age of onset for women and µ2 = average
age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83
years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an
average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of
this disease are normally distributed for each gender, and assume the population variances are equal.
i.
What are the appropriate null and alternative hypothesis?
ii.
What is the value of the test statistics?
iii.
Why you decided to use the test statistics in part ii ?
For a significant level of 0.05, what is the critical value (or critical region)?
What is the appropriate conclusion to this test?
iv.
V.
Transcribed Image Text:Q1.[5 points]: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let µ = average age of onset for women and µ2 = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, and assume the population variances are equal. i. What are the appropriate null and alternative hypothesis? ii. What is the value of the test statistics? iii. Why you decided to use the test statistics in part ii ? For a significant level of 0.05, what is the critical value (or critical region)? What is the appropriate conclusion to this test? iv. V.
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