A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 10 years. A survey of 76 companies reported in The Wall Street Journal found a sample mean tenure of 9 years for CEOs with a standard deviation of s=5.6 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it 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
α=0.10 Your hypotheses are:
Ho:μ≥10
Ha:μ<10
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) α
greater than α
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.
To Test :-
Ho:μ≥10
Ha:μ<10
Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 9 - 10 ) / ( 5.6 / √(76) )
t = -1.557
P - value = P ( t > 1.5567 ) = 0.0619
Looking for the value t = 1.557 in t table across n - 1 = 76 - 1 = 75 degree of freedom.
Decision based on P value
P - value = P ( t > 1.5567 ) = 0.0619
Reject null hypothesis if P value < α = 0.1 level of
significance
P - value = 0.0619 < 0.1 ,hence we reject null
hypothesis
Conclusion :- Reject null hypothesis
The p-value is...less than (or equal to) α
reject the null
There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 10.
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