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Answer:
We conclude that there is no difference between the two classes.
Step-by-step explanation:
We are given that two statistics teachers both believe that each has a smarter class.
A summary of the class sizes, class means, and standard deviations is given below:n1 = 47, x-bar1 = 84.4, s1 = 18n2 = 50, x-bar2 = 82.9, s2 = 17
Let = mean age of student cars.
= mean age of faculty cars.
So, Null Hypothesis, :
{means that there is no difference in the two classes}
Alternate Hypothesis, :
{means that there is a difference in the two classes}
The test statistics that will be used here is <u>Two-sample t-test statistics</u> because we don't know about the population standard deviations;
T.S. = ~
where, = sample mean age of student cars = 8 years
= sample mean age of faculty cars = 5.3 years
= sample standard deviation of student cars = 3.6 years
= sample standard deviation of student cars = 3.7 years
= sample of student cars = 110
= sample of faculty cars = 75
Also, =
= 17.491
So, <u><em>the test statistics</em></u> = ~
= 0.422
The value of t-test statistics is 0.422.
<u>Now, the P-value of the test statistics is given by;</u>
P-value = P( > 0.422) = From the t table it is clear that the P-value will lie somewhere between 40% and 30%.
Since the P-value of our test statistics is way more than the level of significance of 0.04, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as our test statistics will not fall in the rejection region.
Therefore, we conclude that there is no difference between the two classes.