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Anonymous asked in Education & ReferenceHomework Help · 8 years ago

1. What is the sample size necessary to achieve a 90% confidence interval with an allowable error of +-2.5 given that the standard deviation of the population is 4?

2. If A were a Z-score of –0.7, what proportion of the distribution is below A?

3. If A were a Z-score of –0.9 and B were a Z-score of +1.9, what proportion of the distribution is contained between A and B (inclusive)?

4. If the µ (mean) of the above distribution was 5 and A were a Z-score of -2.33, what X score value best represents A (assume the standard deviation is 1 and the sample size is 1)?

5. If the population standard deviation σ of the above distribution was 8 and the µ (mean) of the distribution was 20 and A equaled 15, what proportion of the distribution is above A?

6. Assume a sample size of 40 yielded a mean (X) of 15. Assume the standard deviation of the population is 2.5. What proportion of sample means will be found in repeated experiments to produce a mean of greater than 17.5?

7. Construct a 95% confidence interval for the true population mean () given a sample of size 50 produced a mean (X-bar) of 5 and the population standard deviation is 4. Write your answer in mathematical terms, i.e., C( _______ <  < _______ ) = .9

8. The proportion of scores in a normal distribution expected to occur with a score of less than or equal to the mean score is ___________. The proportion of scores in the normal distribution expected to occur with a score of greater than or equal to the mean score is _. The ratio between these two values is 1 to _.

12. Construct a 90% confidence interval for the true population mean () given that the standard deviation of the population is 16 and the sample mean is 88 and the sample size is 22. State your answer in mathematical terms, i.e., C( _ <  < _ ) = .90

13. It is claimed that the average length of stopping distance measured in feet for Royal tires on cars traveling at 60 mph is 90 feet. A technical engineer runs 23 cars through braking tests and finds the average braking distance of these cars to be 92.5 feet and the sample standard deviation (s) was found to be 6.6 feet. Assume an  value of 0.05. Test the claim by constructing a confidence interval for true population mean .

a) What is the lower-bound of the critical region?

b) What is the upper-bound of the critical region?

c) What is the value of the sample mean?

d) Is the sample mean within the limits of the confidence interval or is the sample mean outside the bounds of the confidence interval?

e) What is your conclusion regarding the claim that cars stop in 80 feet using Royal tires?

f) What support do you have for your conclusion in (e) above?

14. Construct a 90% confidence interval for the true population mean given the data supplied in Question 13. Draw a picture in the box (below) of the distribution, label the appropriate parts, e.g., critical values and regions, etc., and state your critical values in terms of feet (and not in terms of the test-statistic)

a) Now state your confidence interval in mathematical terms, i.e., C( _______ <  < _______ ) = .90

15. Referring to the data in Question 14, what is the value of the “Error” in your confidence interval?

16. It is claimed that 70% of a certain teacher’s students are female. A sample of several classes is done revealing 125 of 200 students of this teacher are females. Construct a 90% confidence interval for the true population proportion of female students for this teacher and state your answer in the correct mathematical way, e.g., HINT: C( _______ < P < _______ ) = .95

17. Continuing with the data in Question #16, test the claim (assume alpha=0.10) by answering the following questions:

a) What is p’ (also known as p-hat)?

b) What is the “Error” of this confidence interval?

c) What is the lower-bound of the estimate of P?

d) What is the upper-bound of the estimate of P?

e) Does the claimed Population proportion (70%) fall within the confidence bounds?

f) Do you accept or reject the claim that the population proportion is 70%?

g) On what basis do you make your decision in (f) above?

h) State your findings in this problem in “English” so a non-statistician will understand what you’ve discovered.

23. It is claimed that the mean number of individuals in a class at Black Hawk College East Campus is not equal to 28. A sample of 15 classes reveals the mean class size to be 27.5 with a standard deviation of 3.5. Construct a 99% confidence interval for the true population mean as a means to test the claim.

a) What is the appropriate statistic to use to test this hypothesis?

b) What is the value of the test-statistic that you used in creating your confidence interval?

c) What is the lower bound of your confidence interval estimate?

d) What is the upper bound of your confidence interval estimate?

e) Does the claimed mean (18) fall within the confidence interval estimate bounds?

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• 8 years ago