Homework SourseA random sample of 15 super bowl MVPs is selected We find th
A random sample of 15 super bowl MVPs is selected. We find that the average age of these 15 super bowl MVPs is 29.13 years with a sample standard deviation of 3.91. We want to determine if the average age of super bowl MVPs differs from the average age of NFL football players in general, which is 27.09 years old. Assume the distribution of the population of ages is normal and use =.05.. A random sample of 15 super bowl MVPs is selected. We find that the average age of these 15 super bowl MVPs is 29.13 years with a sample standard deviation of 3.91. We want to determine if the average age of super bowl MVPs differs from the average age of NFL football players in general, which is 27.09 years old. Assume the distribution of the population of ages is normal and use =.05.
a. What are the null and alternative hypotheses?
b. What is the critical value?
c. Calculate the test statistic.
d. Find the p-value.
e. What conclusion is made here?
Solution
A random sample of 15 super bowl MVPs is selected. We find that the average age of these 15 super bowl MVPs is 29.13 years with a sample standard deviation of 3.91. We want to determine if the average age of super bowl MVPs differs from the average age of NFL football players in general, which is 27.09 years old. Assume the distribution of the population of ages is normal and use =.05.
a. What are the null and alternative hypotheses?
H0: µ = 27.09
H1: µ 27.09
b. What is the critical value?
Table value of t with 14 DF at 0.05 level = 2.1448
c. Calculate the test statistic.
t = \\frac { (\\bar x - \\mu)} {\\frac {s} {\\sqrt{n}}}
t = \\frac{(29.13-27.09)}{\\frac{3.91}{\\sqrt{15}}}
= 2.0207
d. Find the p-value.
P=0.0629
e. What conclusion is made here?
Calculated P = 0.0629 > 0.05 the level of significance
The null hypothesis is not rejected.
There is no evidence to conclude that the average age of super bowl MVPs differs from the average age of NFL football players in general, which is 27.09 years old.
