# Statistics Review

Statistics questions. Please open word document. Missing details attached (got to do with optimal sample size (n)).

Thanks.

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Select the correct answer (letter) to the question from the list of answers on the next page.

1. The ________ is the probability of observing a sample value as extreme as, or more extreme than the value observed, given that the null hypothesis is true.

2. The long-term behavior of a variable over an extended period of time is the ________

3. The variation within a year, such as retail sales during "back to school" period is called ______

4. A period of prosperity, followed by recession is called the ______________

5. When we plot a trend equation, the variable plotted along the horizontal axis is __________

6. Use the __________ to test if two sample variances come from the same or equal populations.

7. The coefficient of correlation can range between the two perfect correlations of ____________

8. If the coefficient of correlation is computed to be -0.80, this means as X increases Y ________

9. In a Chi-Square test of sales by days of the week at the 95% confidence level the critical value is _____.

10. With an r of -0.7 what proportion of the variation in Y is explained by variation in X? ______

11. With the regression equation of Y' = 3X + 25, when X equals 0, then Y' equals _______

12. If we raise the error allowed, E, in our survey results then we can use a _______ sample size, n.

13. The variable plotted on the vertical or Y - axis in a scatter diagram is the _______ variable.

14. If the null hypothesis contains an equal sign, =, then we need to do a _______ tailed test.

15.With a "level of significance" of 0.10, then the "level of confidence" is _________.

16. When the null hypothesis is rejected, we conclude the alternate hypothesis is __________

17. Given the same significance level, a ________ value of t will be required to reject the null hypothesis compared to the value of z required for rejection.

18.With a ________ tailed test the alternative hypothesis contains a < or > sign.

19. The null hypothesis is a claim about the value of the ___________________

20. The t distribution is continuous, has a mean of 0 and is more spread out than the ___________

21. Suggested levels of significance: political polling ______; consumer research ______; and quality control ______.

22. In a one-tailed test at alpha 0.05, with n = 21: z critical is ______; and t critical is_______.

23. To determine the equation for the regression line you (or Excel) use the ___________method.

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FILL-IN QUESTIONS

1. In Week 1 of RES/342 we 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

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PROBLEMS (For full credit be sure to show your work.)

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

Select the correct answer (letter) to the question from the list of answers on the next page.

1. The p-value (d) is the probability of observing a sample value as extreme as, or more extreme than the value observed, given that the null hypothesis is true. You want a low p-value, in order to minimize the chances of rejecting the null hypothesis when it is actually true (this is an example of a type I error).

2. The long-term behavior of a variable over an extended period of time is the secular trend (h)

3. The variation within a year, such as retail sales during "back to school" period is called seasonal variation (n)

4. A period of prosperity, followed by recession is called cyclical variation (m)

5. When we plot a trend equation, the variable plotted along the horizontal axis is time(x). In general, you plot the independent variable on the horizontal axis.

6. Use the F-distribution (p) to test if two sample variances come from the same or equal populations.

7. The coefficient of correlation can range between the two perfect correlations of -1 and 1 (u).

8. If the coefficient of correlation is computed to be -0.80, this means as X increases Y decreases (i). You can tell because the coefficient is negative.

9. In a Chi-Square test of sales by days of the week at the 95% confidence level the critical value is 12.59 (g). Use df = 7 - 1 = 6.

10. With an r of -0.7 what proportion of the variation in Y is explained by variation in X? 49% (y) Square -0.7 to get 0.49. This gives you 49%.

11. With the regression equation of Y' = 3X + 25, when X equals 0, then Y' equals 25 (v). Just plug x = 0 into the equation.

12. If we raise the error allowed, E, in our survey results then we can use a smaller (z) sample size, n.

13. The variable plotted on the vertical or Y - axis in a scatter diagram is the dependent (f) variable.

14. If the null hypothesis contains an equal sign, =, then we need to do a two (w) tailed test.

15.With a "level of significance" of 0.10, then the "level of confidence" is 0.90 (t). This is 1 minus the type I error level: 1 - 0.10 = 0.9.

16. When the null hypothesis is rejected, we conclude the alternate hypothesis is true (b). Actually, you say you accept the alternate hypothesis, but technically, you can't say that the alternative hypothesis is true.

17. Given the same significance level, a higher (j) value of t will be required to reject the null hypothesis compared to ...