Answer:
Margin of error = ±1.96*std error
= ±1.1479
Confidence interval = Mean ±1.1479
=[tex](5.8521, 8.1479)[/tex]
Step-by-step explanation:
given that a random sample of 41 car owners results in a mean of 7
years.Assume a population a standard deviation of 3.75 years.
By central limit theorem we can say sample mean will have point estimate as 7 and std error as = [tex]\frac{3.75}{\sqrt{41} } \\=0.586[/tex]
Since population std deviation is known and sample size >30 and also random is assured we can use Z critical value for finding out the margin of error.
95% Z critical value = ±1.96
Margin of error = ±1.96*std error
= ±1.1479
Confidence interval = Mean ±1.1479
=[tex](5.8521, 8.1479)[/tex]
