I am not sure how to do problem 4 pictured here. 1. Working for a car company, y
ID: 3048617 • Letter: I
Question
I am not sure how to do problem 4 pictured here.
1. Working for a car company, you have been assigned to find the average miles per gallon (mpg) for a certain model of car. You take a random sample of 49 cars of the assigned model. The observed sample mean is 26.7 mpg. Based on previous evidence and a QQ plot, you have reason to believe that the gas mileage is normally distributed with standard deviation sd) 6.2 mpg. (a) Construct and interpret 95% confidence interval for the mean mpg, p. fr the certain model of car. (b) What would happen to the interval if you increased the confidence level from 95% to 99%? Explain your reasoning. (Do not compute the new interval.) (e) Suppose you are asked to repeat this process with data gathered from all across the country. You end up constructing a total of 60 separate 95% confidence intervals at different factories for the estimated average mpg of the model of car. Of these intervals, how many of them do you expect would fail to contain the true value of ? (d) Now suppose based on previous evidence, it is not clear that the gas mileage is normally d But you know the distribution is approximately symmetric with the same mean and sd. Then does the confidence interval for . found in (a), remain valid? Give reasons.Explanation / Answer
a)
sample mean = 26.7 , n = 49 , s = 6.2
using t- distribution
df =n-1= 48
t-critical for 95 % confidence = 2.010635 {=T.INV.2T(0.05,48)}
(Xbar - t * s/sqrt(n) , Xbar + t * s/sqrt(n) }
=(26.7 - 2.010635 *6.2/sqrt(49) ,26.7 + 2.010635 *6.2/sqrt(49)}
= (24.919151 ,28.480848)
b)
when we increase confidence level, confidence interval becomes wider
as t-critical increases as confidence level increase
c)
we expect 60 * 0.95 = 57
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