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

Answer:

Both have mid value of interval as mean =2.98

Step-by-step 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