The Motor Vehicle Manufacturers Association is interested in whether, on average
ID: 3314162 • Letter: T
Question
The Motor Vehicle Manufacturers Association is interested in whether, on average, a new SUV is kept at least 4 years by its first owner before selling it or trading it in. Assume that lengths of time a new SUV is kept by its first owner are approximately normally distributed. A random sample of 31 purchases of a new SUV is taken. In this sample, the mean length of time the SUV was kept was 3.8 years, and the standard deviation of lengths of time the SUV’s were kept was .6 year. Test the null hypothesis that the mean length of time the first owner keeps a new SUV is at least 4 years, against the alternative hypothesis that it is less. Use a 5% level of significance.
MULTIPLE CHOICE #14 What are the test statistic and its sampling distribution? a. X ~ N 0,1 n by the CLT since n = 61 is large b. X ~ N 0,1 n because the population is normal c. n 1 X ~ t S n by the CLT since n = 61 is large d. n 1 X ~ t S n because the population is normal and is unknown
MULTIPLE CHOICE #15 (Continued) What is the value of cv (the critical value)? a. 4 c. 3.82 b. 3.85 d. 3
MULTIPLE CHOICE #16 (Continued) What is the conclusion of the test? a. Accept H0 b. Reject H0 in favor of HA
Explanation / Answer
we are given
n = 31
xbar = 3.8
mu = 4
sd = 0.6
the t stat is calculated as
t = (xbar-mu)/(sd/sqrt(n))
= (3.8-4)/(0.6/sqrt(31))
= -1.855
so we first calculate the cv from the t table
for alpha = 0.05 ,
df = n-1 = 31-1 = 30
and 1 tail , as we are interested in the "at least 4 years " part of the claim
t-value (right-tail): 1.697
as the t critical is greater than t stat hence we fail to reject the null hypothesis
I dont think the multiple questions correspond to the main question given . However , the above calculations for the main questions are correct