Question

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk, what similarities would they have?

Answer 1

Both have mid value of interval as mean =2.98

Explanation:

Given that a survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10.

We have Margin of error =
`Z_(critical )`* Std error

The critical values for z are as per table below:

Confidence level Z critical Margin of error

90% 1.645
`1.645*0.1=0.1645`

95% 1.96
`1.96(0.1) = 0.196`

Mean of milk galon = 2.98

Confidence interval =
`2.98`±Margin of error

CI 90% =
`(2.98-0.1645, 2.98+0.1645)\\=(2.8155, 3.1445)`

CI 95% =
`(2.98-0.196, 2.98+0.196)\\= (2.784, 3.176)`

Similarities are both have mid value the same as 2.98