Exercises. 1. Determine a 90 % confidence interval for if , ,

1. Determine a 90 % confidence interval for if , ,

and .

2. Determine a 98 % confidence interval for if , ,

and .

3. A sample of size 50 from a population yielded the sample values ,

and Find a 95 per cent confidence interval for .

4. For a sample data set, , and

a) Construct a 95 % confidence interval for assuming n = 50.

b) Construct a 90 % confidence interval for assuming n = 50. Is the width of the 90 % confidence interval smaller than the width of the 95 % confidence interval calculated in part a? If yes, why it is so?

c) Find a 95% confidence interval for assuming n = 100. Is the width of the 95 % confidence interval for with n = 100 smaller than the width of the 95 % confidence interval for with n = 50 calculated in part a?

If so, why?

5.

a) A sample of 100 observations taken from a population produced a sample mean equal to 55.32 and a standard deviation equal to 8.4. Make a 90 % confidence interval for .

b) Another sample of 100 observations taken from the same population produced a sample mean equal to 57.40 and a standard deviation equal

to 7.5. Make a 90 % confidence interval for .

c) A third sample of 100 observations taken from the same population produced a sample mean equal to 56.25 and a standard deviation equal

to 7.9. Make a 90 % confidence interval for .

d) The true population mean for this population is 55.80. How many of the confidence intervals constructed in a-c cover this population mean and how many do not?

6. The mean annual salaries of managers at the certain company is $80 722 for males and $65 258 for females. These mean salaries are based on samples of 400 male and 200 female managers. Assume that the standard deviation of the annual salaries of male managers is $11 500 and standard deviation of the female managers is $8 400.

a) Construct a 95 % confidence interval for the mean annual salary of male managers.

b) Construct a 95 % confidence interval for the mean annual salary of female managers.

7. From a random sample of 70 high school seniors, the sample mean and standard deviation of the math scores are found to be 96 and 17 respectively. Determine a 96% confidence interval for the mean math score of all seniors in the school.

8. With a random sample of size n =144, someone proposes

to be a confidence interval for . What then is the level of confidence?

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