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MidtermI_-2_25_2008_sol

# MidtermI_-2_25_2008_sol - Midterm Exam#1 2008 Stat 102...

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1 Midterm Exam #1, 2008, Stat 102 Solutions Sections: 001 = M&[email protected]:30; 002 = T&[email protected]:30; 003 = T&[email protected]:30 Instructions : This is a semi-closed book exam. Up to two pages of notes are allowed. (These two pages may be two-sided if you wish.) When performing hypothesis tests, clearly state the null and alternative hypotheses and show the critical value and/or P-value (from the table) where appropriate. Normal tables, t tables and F tables are provided, as needed. Write your answers on the test and always show your work. Partial credit will be given. Time: 90 minutes . Your Name ____________________________ Section #: 001 (Prof. Brown) _______ 002 (Prof. Zhao) _______ 003 (Prof. Zhao) _______ Sections: 001 = M&[email protected]:30; 002 = T&[email protected]:30; 003 = T&[email protected]:00 Point Allocations are indicated for each numbered problem (out of 100 total points).

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2 1. [20 Points] It is often claimed that blood pressure increases with age. Here is some data about Systolic Blood Pressure for a sample of females at age 48 and at age 58. Here are the side- by-side boxplots and summary statistics for the 48 year olds and for the 58 year olds. 100 150 200 250 SBP 48 58 AGE Age Number Mean Std Dev Std Err Mean 48 41 142.85 20.48 3.198 58 37 157.14 33.38 5.488 Here is some JMP output for tests of equality of blood pressure among the two age groups: Assuming equal variances Difference 14.282 t Ratio 2.302 Std Err Dif 6.204 DF 76 Not Assuming equal variances Difference 14.282 t Ratio 2.248 Std Err Dif 6.352 DF 58.5 (a) Conduct a suitable test of the null hypothesis that the two groups have equal mean blood pressures. Give the (approximate) P- value of the test. Can you conclude at α = 0.05 that the two groups have different mean blood pressures? Can you conclude this to be so at level α = 0.01? SOLUTION: Since the larger of the larger ratio of 2 2 2 2 1 2 / 33.38 / 20.48 2.67 3 s s , we may take the equal variance assumption. So the t ratio is 2.3 with df=76. This results in a p-value of 2*P(Z>2.3)=2*.0107=.02. We will reject the null hypothesis at α = 0.05 but not at α = 0.01.