Answer:
The lower limit for a 98% confidence interval for the population mean is 79.40.
Step-by-step explanation:
Given : To estimate the average students' scores in a standardize test, a sample of 35 scores yielded a mean of 80 and a standard deviation of 9.
To find : What is a lower limit for a 98% confidence interval for the population mean?
Solution :
The confidence interval formula is given by,
[tex]CI=\bar{x}\pm Z_c(\frac{\sigma}{n})[/tex]
The lower limit is [tex]CI=\bar{x}-Z_c(\frac{\sigma}{n})[/tex]
Where, [tex]\bar{x}=80[/tex] is the mean
[tex]\sigma=9[/tex] is the standard deviation
n=35 is the number of element
[tex]Z_c[/tex] at 98% is 2.33.
Substitute all values in the formula,
[tex]CI=80-(2.33)(\frac{9}{35})[/tex]
[tex]CI=80-(2.33)(0.257)[/tex]
[tex]CI=80-0.59881[/tex]
[tex]CI=79.40[/tex]
Therefore, The lower limit for a 98% confidence interval for the population mean is 79.40.
