Question

I need help with questions A-1 and B-1.

Thanks

Consider the following hypotheses: HO: u = 120 HA: U 120 The population is normally distributed with a population standard deviation of 46. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic with x = 132 and n = 50. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) % Answer is complete but not entirely correct. Test statistic (2.63 X a-2. What is the conclusion at the 5% significance level? Reject Ho since the p-value is less than the significance level. Reject Ho since the p-value is greater than the significance level. Do not reject Ho since the p-value is less than the significance level. Do not reject Ho since the p-value is greater than the significance level. a-3. Interpret the results at a = 0.05. We conclude that the population mean differs from 120. We cannot conclude that the population mean differs from 120. We conclude that the sample mean differs from 120. We cannot conclude that the sample mean differs from 120. b-1. Calculate the value of the test statistic with x = 108 and n = 50. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic

Answer 1

Solution:

Given:

$H_{0}: \mu = 120$

На : д2 120

Population Standard Deviation = $\sigma = 46$

Part a-1:

$\bar{x} = 132$

n = 50

Test statistic:

$z=\frac{\bar{x}-\mu }{\sigma /\sqrt{n}}$

$z=\frac{132-120 }{ 46 /\sqrt{50}}$

$z=\frac{ 12 }{ 46 /7.071068 }$

$z=\frac{ 12 }{ 6.505382 }$

$\mathbf{{\color{DarkOrange} z=1.84}}$

Part b-1)

Given:

$\bar{x} = 108$

n = 50

Test statistic:

$z=\frac{\bar{x}-\mu }{\sigma /\sqrt{n}}$

$z=\frac{ -12 }{ 46 /\sqrt{50}}$

$z=\frac{ -12 }{ 46 /7.071068 }$

$z=\frac{ -12 }{ 6.505382 }$

$\mathbf{{\color{DarkBlue} z=-1.84}}$