Answer:
Hence, in this case, the 98% confidence interval would be (163.626;180.374)
Step-by-step breakdown:
Previous concepts
A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.
The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.
A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.
denote the sample mean
population mean (the variable of interest)
s=16 signifies the sample standard deviation
n=23 represents the sample size
The solution to the query
The equation for the confidence interval of the mean is given by the following formula:
(1)
To determine the critical value , we first need to calculate the degrees of freedom, which is expressed as:
Since the confidence level is 0.98 or 98%, we find the value of and
using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields
Having all components ready, we can substitute into formula (1):
Thus, for this case, the 98% confidence interval will be (163.626;180.374)