Question

The shareholders group claimed that the mean tenure for a chief executive office (CEO) was less than 10 years. A survey of 36 companies were sampled and the mean tenure was 9.5 years with a standard deviation of 5.3 years. Assume the data is normally distributed.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of 0.010.01.

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 10.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 10.
• The sample data support the claim that the population mean is less than 10.
• There is not sufficient sample evidence to support the claim that the population mean is less than 10.

Answer 1

Solution : -

Given that ,

= 10

= 9.5

s = 5.3

n = 36

The null and alternative hypothesis is ,

H0 :   = 10

Ha : < 10

This is the left tailed test .

Test statistic = T

= ( - ) / s / n

= ( 9.5 - 10 ) / 5.3 / 36

= -0.566

The test statistic = -0.566

df = n - 1 = 36 - 1 = 35

P-value = ( t -0.566 , 35 )

= 0.2875

P - value = 0.2875

= 0.01

0.2875 > 0.01

P-value >  

The P - value is greter than  

Fail to reject the null hypothesis .

Conclusion : -

• There is not sufficient sample evidence to support the claim that the population mean is less than 10.