08Ma2bHw7Sol

# 08Ma2bHw7Sol - MA2B HOMEWORK 7 SOLUTIONS Problem 1 Denote...

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MA2B HOMEWORK 7 SOLUTIONS Problem 1. Denote the pulse rates measured before the program by X i (1 i 7), and those measured after one month by Y i (1 i 7). Assume that the pairs ( X i ,Y i ) are independent and the diFerences D i = X i - Y i are distributed N ( μ,σ 2 ), where μ and σ are unknown. A positive μ indicates that jogging lowers pulse rate, so we shall test H : μ 0 vs. K : μ> 0 . We will use the paired t test: see page 14 of the Hypothesis Testing notes. Our test statistic is t = D 7 S/ 7 , where D 7 is the sample mean and S is the sample standard deviation of D i ’s. This statistic has the student t distribution with 7 - 1 = 6 degrees of freedom; see page 7 of the Hypothesis Testing notes. So at signi±cance level α =0 . 05, we should reject H if t t 6 , 0 . 95 =1 . 943 . The observed data is D 1 =4 ,D 2 3 =8 4 =7 5 6 = 10 7 = - 2 D 7 =5 ,S =3 2 . Therefore t = D 7 S/ 7 . 118 > 1 . 943 . Hence we reject the null hypothesis and conclude that regular jogging lowers one’s pulse rate. Problem 2. (a) If the 7 “Before” measurements and the 7 “After” ones were given without any pairings, then we would assume the two samples were independent and use the 2-population t test. (b) Let X i , Y i (1 i 7) be the same as in problem 1. Assume X i ’s and Y i ’s are independent and X i ’s are i.i.d. N ( μ X 2 ), while Y i ’s are i.i.d. N ( μ Y 2 ). As μ X Y indicates that jogging lowers pulse rate, we are going to test H : μ X μ Y vs. K : μ X Y .

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## This note was uploaded on 01/08/2011 for the course MA 2b taught by Professor Makarov,n during the Winter '08 term at Caltech.

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08Ma2bHw7Sol - MA2B HOMEWORK 7 SOLUTIONS Problem 1 Denote...

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