Question

The first picture contains the whole math problem. The second picture contains only b which I need the answer for. The p-value has a dropdown option sonesse choose the correct answer from there. THANKS IN ADVANCE!!!

companies reported in the Wall Street A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least seven years. A survey of Journal found a sample mean tenure of 6.68 years for CEOs with a standard deviation of 7.31 years a. Formulate hypotheses that can be used to challenge the validity of the daim made by the shareholders' group. b. Assume 65 companies were included in the sample. what is the p-value for your hypothesis test? Enter negative value as negative number t-value(to 3 decimals) p-value 1 -Selet your answer c. At 0.02, what is your conclusion Select your answer the null hypothesis. We Select our anwwerenough evidence to disprove the shareholder group's diaim.

Answer 1

Solution:

Given:

Sample size = n = 65

Sample Mean = $\bar{x}=6.68$

Sample Standard Deviation = s = 7.31

We have to test if the mean tenure for a chief executive office (CEO) is at least 7 years.

Part a) state H0 and Ha:

$H_{0}: \mu \geq 7$

$H_{a}: \mu < 7$

Part b) To find the p-value, we need to find t test statistic value:

$t=\frac{\bar{x}-\mu }{s /\sqrt{n}}$

$t=\frac{6.68-7 }{7.31 /\sqrt{65}}$

$t=\frac{-0.32 }{7.31 /8.06226 }$

$t=\frac{-0.32 }{0.90669 }$

$t=-0.353$

p-value:

df = n - 1 = 65 - 1 = 64

Use following excel command to get p-value:

=T.DIST( x , df , cumulative)

=T.DIST( -0.353 , 64 , TRUE)

=0.3626

Thus p-value greater than 0.20 is correct choice.

We can use t table as below:

df = 64 is not listed in t table, so we look for its previous df = 60 row and find interval in which absolute t = 0.353 fall.

and then we find corresponding one tail area( since this is one tailed test) for p-value interval.

From above t table, t = 0.353 fall in between 0.000 and 0.679 and it corresponds to one tail area between 0.25 and 0.50

Thus p-value interval is 0.25 to 0.50

That is p-value is greater than 0.20

Part c)

Since p-value > 0.20 which means p-value > 0.02 level of significance , hence we failed to reject null hypothesis.

Thus we get:

Fail to reject the null hypothesis, we do not have enough evidence to disprove the shareholders group claim.