Question

A random sample of 41 car owners results in a mean of 7

years.Assume a population a standard deviation of 3.75 years. Find
a 95 %confidence interval for the true population mean. Identify
thepoint estimate for the mean and margin of error. Using this
infofind a 95% confidence interval for the population variance
andstandard deviation. Identify the point estimates for both.

Answer 1

Margin of error = ±1.96*std error

= ±1.1479

Confidence interval = Mean ±1.1479

=
`(5.8521, 8.1479)`

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 =
`(3.75)/(√(41) ) \\=0.586`

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

=
`(5.8521, 8.1479)`