Answer:
We conclude that the Escalade buyers are younger on average than the typical Cadillac buyer.
Step-by-step explanation:
We are given that the average Cadillac buyer is older than 60, past the prime middle years that typically are associated with more spending.
A sample of 50 Escalade purchasers has average age 45 (with standard deviation 25).
Let = <u><em>average age of an Escalade buyers.</em></u>
So, Null Hypothesis, :
60 {means that the Escalade buyers are are of equal age or older on average than the typical Cadillac buyer}
Alternate Hypothesis, :
< 60 {means that the Escalade buyers are younger on average than the typical Cadillac buyer}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean age of Escalade purchasers = 45
s = sample standard deviation = 25
n = sample of Escalade purchasers = 50
So, <u><em>the test statistics</em></u> = ~
= -4.243
The value of t test statistics is -4.243.
<u>Now, at 0.05 significance level the t table gives critical value of -1.677 at 49 degree of freedom for left-tailed test.</u>
Since our test statistic is less than the critical value of t as -4.243 < -1.677, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the Escalade buyers are younger on average than the typical Cadillac buyer.