Question

HW#9 - Chapter 18 (20pts for turned in on time) 1. (16pts, 2pts each)In most of the practical problems, we don't know population standard deviation. Sot test is much more useful than z test, since it doesn't require a known population standard deviation. For the following scenario, please provide the appropriate p value (keep in mind that p-value is always dependent on the alternative hypothesis Ha). (1) Ha:> , sample size = 10, and t = 3.576 (2) Ha: > Ho, sample size = 15, and t = 2.253 (3) Ha: <Ho, sample size = 17, and t = -3.564 (4) Ha: <H, sample size = 13, and t = 2.145 (5) Ha: 4 * Ho, sample size=24, and t - 3.002 (6) Haru* Ho, sample size = 20, and to -3.156 (7) Ha:* Ho, sample size = 2000, and t-3.156 (8) Ha: u > Ho, sample size = 26, and t=2.432

Answer 1

1) Given Ha : $\mu$ > $\mu$ o , sample size n = 10 , t = 3.576

here degrees of freedom = n - 1 = 9

p-value = P( t > 3.576) d.f = 9

p-value = 0.0030

2) Ha : $\mu$ > $\mu$ o , n = 15 , t = 2.253

d.f = n-1 = 14

p-value = P( t > 2.253 ) d.f = 14

p-value = 0.0204

3) Ha :  $\mu$ < $\mu$ o , n = 17 , t = -3.564

d.f = n - 1 = 16

p-value = P( t < -3.564) d.f = 16

p-value = 0.0013

4) Ha : $\mu$ < $\mu$ o , n = 13 , t = 2.145

d.f = n - 1 = 12

p-value = P( t < 2.145 ) d.f = 12

p-value = 0.9734