# Statistics Questions and Answers

1. Since we have determined the optimal sample size, n, using a three variable formula. Fill in the following table listing the three variables and specify the effect on n (either + or -) of increasing and decreasing each variable, one at a time.

VARIABLE EFFECT of INCREASE EFFECT of DECREASE

2. Given a Chi-Square problem where the sum of the observed frequencies (first column) is 500, the sum of the expected frequencies (second column) should equal _________and the sum of the observed frequencies minus the expected frequencies (third column) should equal _________.

3. Given a two-tailed hypothesis test where n = 40, the desired level of confidence is 95% and the population standard deviation is known, we would use the ______ test for the ______ level of significance and the critical value of __________.

4. Given an upper tail hypothesis test where n = 25, the desired level of confidence is 90% and the population standard deviation is unknown, we would use the ______ test for the ______ level of significance and the critical value of __________.

5. If the value of the test statistic falls in the "rejection region", our data are inconsistent with _______ and the decision should be to accept the _____________.

6. Degrees of freedom in a Chi-Square problem is dependent upon the number of _____________ while degrees of freedom in an F Distribution problem is dependent on _____________ in both the ___________________ and the _____________________.

7. Please fill in the second table given a 0.05 level of significance and the following data:

ROUTE MEAN TIME STANDARD DEVIATION OBSERVATIONS

Freeway 40 minutes 3 minutes 12 commuters

Surface Streets 45 minutes 5 minutes 8 commuters

Numerator Denominator Degrees of Freedom Numerator Degrees of Freedom Denominator F Critical Value Factor(s) & Levels Response Variable

Please explain how to solve the problems below

1.Your company wants to conduct a salary survey for the position of Accounting Assistant II. The estimated salary range is $4,500, the margin of error should be $100 and the desired level of confidence is 95%. What is the optimal sample size for this salary survey?

_______________

2. A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in the sample mean of $220 and a sample standard deviation of $12. The researchers have determined that they should test that the mean bill exceeds $200 at the 5% level of significance.

What is the Null Hypothesis? ___________

What is the Alternate Hypothesis? ____________

How many tail(s) in the test? __________

What test should the researchers use? _________________

Why do they use this test?

______________________________________________________________________________________

______________________________________________________________________________________

What is the critical value? ________________

If the calculated value for the test statistic is 5.77, then what have the researchers learned with the test?

______________________________________________________________________________________

Are the test results reliable?

#### Solution Summary

Filling in the blanks on Chi-square, hypothesis, samples sizes, and more. No discussion (except for one question where an explanation is requested), only answers to complete the sentences.