# 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 Preview

See attached file.

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

 + -

 - because z decreases + because z increases

d - +

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 500 and the sum of the observed frequencies minus the expected frequencies (third column) should equal 0.

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 z test for the 0.05 level of significance and the critical value of +1.96 and -1.96.

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 t test for the 0.1 level of ...

#### 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.