Question

A random sample of 49 text books purchased at a local bookstore showed an average price of $122 with a population standard deviation of $15. Let u (new) be the true mean cost of a text book sold by this store. Construct a confidence interval with a 90% degree of confidence. Clearly label the following:

a. Point estimate
b. Critical value,
c. Margin of error
d. Confidence interval
e. Interpretation (confidence statement).

Answer 1

1. point estimate is $122
2. critical value for the 90% confidence level (1.645)
3. margin of error is $3.525
4. 90% confidence interval is $122±3.525
5. there is 90% probability that true population average price of text books is in the range $122±$3.525

Explanation:

Confidence Interval can be calculated using P±ME where

• P is the point estimate for the mean cost of a text book ( $122 )

• ME is the margin of error from the mean

And margin of error (ME) can be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the critical value for the 90% confidence level (1.645)

• s is the population standard deviation ($15)

• N is the sample size (49)

Margin of error, ME=
`(1.645*15)/(√(49) )` = 3.525

Then 90% confidence interval is $122±3.525

To interpret this, there is 90% probability that true population average price of text books is in the range $122±$3.525