Question

#5.

1. Compute the value of the test statistic for the indicated test, based on the information given.

   1. Testing H0:μ=72.2H0:μ=72.2 vs. Ha:μ>72.2Ha:μ>72.2, σ unknown, n = 55, x⎯⎯=75.1x-=75.1, s = 9.25
   2. Testing H0:μ=58H0:μ=58 vs. Ha:μ>58Ha:μ>58, σ = 1.22, n = 40, x⎯⎯=58.5x-=58.5, s = 1.29
   3. Testing H0:μ=−19.5H0:μ=−19.5 vs. Ha:μ<−19.5Ha:μ<−19.5, σ unknown, n = 30, x⎯⎯=−23.2x-=−23.2, s = 9.55
   4. Testing H0:μ=805H0:μ=805 vs. Ha:μ≠805Ha:μ≠805, σ = 37.5, n = 75, x⎯⎯=818x-=818, s = 36.2

Answer 1

5)

a)

The test statistic is given by:

T- t: 75.1 - 72.2 9.25 5 = 2.325 | | 71

{t-statistic because population standard deviation is not known}

b)

The test statistic is given by:

$z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{58.5-58}{\frac{1.22}{\sqrt{40}}}=2.592$

{z-statistic because population standard deviation is known}

c)

The test statistic is given by:

$t=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{-23.2-(-19.5)}{\frac{9.55}{\sqrt{30}}}=-2.122$

{t-statistic because population standard deviation is not known}

d)

The test statistic is given by:

$z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{818-805}{\frac{37.5}{\sqrt{75}}}=3.002$

{z-statistic because population standard deviation is known}