Question

Consider the following hypotheses: Hot 208 RAM 208 A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. (You may find it useful to reference the appropriate table: z table or table) a-1. Calculate the value of the test statistic. (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 a-2. Find the p-value. O p-value 20.10 O p-value < 0.01 O 0.01 s p-value < 0.025 O 0.025 s p-value <0.05 O 0.05 s p value < 0.10

Answer 1

Solution:

Given

n = 74 sample size

$\bar x= 202$. Sample mean

$\mu= 208$. Population mean

$\sigma= 26$. Population standard deviations.

To test the hypothesis

$Ho:\mu\geq 208$. Vs. $Ha:\mu< 208$

a-1) Test statistic

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

$Z=\frac{202-208}{26/\sqrt 74}$

$Z=\frac{202-208}{26/8.6023}$

$Z=\frac{-6}{3.0224}$

Z = -1.9851773

Test statistic Z = -1.99

a-2) P Value = 0.0233 from Z table

0.01 < P Value < 0.025

Option C is correct

b) Decision

P Value < $\alpha=0.10$

Reject Ho .

The above sample give evidence to Reject the null hypothesis at $\alpha=0.10$

since the P value less than the significance level

Option A is correct.

c) Decision at.$\alpha=0.01$

P Value > $\alpha=0.01$

Fail to reject Ho.

The above sample does not give evidence to Reject the null hypothesis at $\alpha=0.01$

Since P Value is greater than the significance level .

Option A is correct.

d) Interpretation of the results at $\alpha=0.01$

We can not conclude that population mean is less than 208

Option A is correct.