Answer:
The 90% confidence interval would be given by (110.168;117.832)
The 95% confidence interval would be given by (119.393;118.607)
Step-by-step explanation:
Assuming this info:" A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% and 95 confidence interval for the population mean".
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s=15.30 represent the sample standard deviation
n=45 represent the sample size
2) 90% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are given by:
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,44)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (110.168;117.832)
3) 95% confidence interval
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,44)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (119.393;118.607)