A study is conducted among a group of soccer coaches. A random sample of 98 soccer coaches reveals that
their average salary is $85,500. Historically, the population standard deviation of the salary of soccer
coaches is $3,700.
Round the critical values to 3 decimal places and the confidence interval values to 2 decimal places.
For part (a), use a positive critical value and NOT a negative value.
Construct a 96% confidence interval for the mean salaries of all soccer coaches.
(a) What is the critical value that will need to be used to calculate the confidence interval?
(b) What is the 96% confidence interval?
<mu <
(c) Interpret your result above:
There is a 96% chance that out of all possible sample mean salaries for all soccer coaches, that the
sample mean is contained in the confidence interval in part (b).
We can be 96% confident that the population mean salary for all soccer coaches is contained in the
confidence interval in part (b).
We can be 96% confident that the mean salary for the sample of 98 soccer coaches is contained in
the confidence interval in part (b).
There is a 96% chance that out of all possible population mean salaries for all soccer coaches, that
the true mean is contained in the confidence interval in part (b).
None of the above.
If the researcher wants to be 98% confident that the sample mean is within $695 of the true population
mean, how many soccer coaches should be included in the sample?
(d) What is the critical value that will need to be used to calculate the sample size?
(e) What is the sample size requiredi
A study is conducted among a group of soccer coaches. A random sample of 98 soccer coaches reveals that their average salary is $85,500. Historically, the population standard deviation of the salary of soccer coaches is $3,700.
Round the critical values to 3 decimal places and the confidence interval values to 2 decimal places.
For part (a), use a positive critical value and NOT a negative value. Construct a 96% confidence interval for the mean salaries of all soccer coaches.
(a) What is the critical value that will need to be used to calculate the confidence interval?
(b) What is the 96% confidence interval?
(c) Interpret your result above:
O There is a 96% chance that out of all possible sample mean salaries for all soccer coaches, that the sample mean is contained in the confidence interval in part (b). O We can be 96% confident that the population mean salary for all soccer coaches is contained in the confidence interval in part (b). O We can be 96% confident that the mean salary for the sample of 98 soccer coaches is contained in the confidence interval in part (b). O There is a 96% chance that out of all possible population mean salaries for all soccer coaches, that the true mean is contained in the confidence interval in part (b). O None of the above.
If the researcher wants to be 98% confident that the sample mean is within $695 of the true population mean, how many soccer coaches should be included in the sample?
(d) What is the critical value that will need to be used to calculate the sample size?
(e) What is the sample size required?