A consulting firm claims that the average age of millionaires in the US is under 55 years. To test this claim, a random sample of 30 millionaires was selected. The ages of those random millionaires are shown on the template.
40 |
51 |
60 |
25 |
30 |
55 |
76 |
61 |
38 |
65 |
78 |
54 |
50 |
74 |
80 |
27 |
67 |
42 |
46 |
26 |
55 |
40 |
78 |
48 |
46 |
33 |
31 |
80 |
57 |
49 |
A) state the appropraite null and alternative hypotheses.
B.)which test statistic do you use?
C.) what is the critical value of that test statistic, using a 0.01 significance leve?
D.) what is your decision rule?
E.) what is the calcualted value of the test statistic?
F.) do you reject or fail to reject the null hypothesis>
G.) what is your conclusion about the average age of millionares?
H.) calculate the p-value of this test and clearly state its meaning
Claim : The average age of millionaires in the US is under 55 years.
A) null and alternative hypotheses.
H0 : µ = 55 vs Ha : µ < 55
We can find sample mean and sample standard deviation using excel function =AVERAGE( data set) and =STDEV.S( data set) respectively.
Therefore , = 52.0667 and s = 17.1885
B) Population standard deviation σ is unknown therefore we use t test statistic.
C) Critical value:
given α = 0.01
As Ha contain < sign , this is left tail test,therefore critical value would be negative.
d.f = n-1 = 30-1 =29
We can find critical value using excel function, =TINV(2*α ,d.f )
=TINV(2*0.01 ,29 ) = 2.462
Critical value = -2.462
D) Decision rule :
Reject H0, if t test statistic ≤ -2.462 Or fail to reject H0 , if t test statistic > -2.462
E) Test statistic:
t = =
t = -0.93
F) Decision: As t test statistic is greater than -2.462, we fail to reject H0
G) Conclusion: There is no significant evidence that the average age of millionaires in the US is under 55 years.
H) To find p-value we can use excel function =TDIST( t , d.f , tail ) ( note : use positive value of t and for one tail test plug 1 for tail , for two tail test plug 2 for tail )
=TDIST(0.93,29,1)
P-value = 0.1800
Interpretation of p-value : The probability that sample mean is less than 52.0667 is equal to 0.1800, under the H0 : µ = 55
A consulting firm claims that the average age of millionaires in the US is under 55...
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