Hypothesis Testing:Mean,Correlation, ANOVA

1. To determine if a diet supplement is useful for increasing weight, patients are weighed at the start of the program and at the end of the program. This is an example of
a. test of paired differences. b. independent sample.
c. one-sample test for means. d. two-sample test for means.

2. The analysis of variance technique is a method for
a. comparing three or more means. b. comparing F distributions.
c. measuring sampling error. d. none of the above.

3. A treatment is
a. a normal population. b. the margin of error.
c. a source of variation. d. the amount of random error.

4. In a one-way ANOVA, k refers to the
a. number of observations in each column. b. the number of treatments.
c. the total number of observations. d. none of the above.

5. The F distribution is
a. a continuous distribution. b. based on two sets of degrees of freedom.
c. never negative. d. all of the above

6. In an ANOVA test there are 5 observations in each of three treatments. The degrees of freedom in the numerator and denominator respectively are:
a. 2, 4 b. 3, 15 c. 3, 12 d. 2, 12

7. Which of the following assumptions is not a requirement for ANOVA?
a. dependent samples b. normal populations
c. equal population variances d. independent samples

8. Which of the following statements is not correct regarding the coefficient of correlation.
a. It can range from 1 to 1.
b. Its square is the coefficient of determination.
c. It measures the percent of variation explained.
d. It is a measure of the association between two variables.

9. The coefficient of determination
a. is usually written as r2. b. cannot be negative.
c. is the square of the coefficient of correlation. d. all of the above.

10. The coefficient of correlation between two variables X and Y was computed to be 0.60. This means
a. the coefficient of determination is 0.
b. as X increases Y decreases.
c. X and Y are both 0.
d. as X decreases Y decreases.

11. A regression equation is used to
a. measure the association between two variables.
b. estimate the value of the dependent variable based on the independent variable.
c. estimate the value of the independent variable based on the dependent variable.
d. estimate the coefficient of determination.

Q2(0.5 points): For each of the following situations, indicate whether an error has occurred and, if so, indicate what kind of error (Type I or Type II) has occurred.
a We do not reject H0 and H0 is true.
b We reject H0 and H0 is true.
c We do not reject H0 and H0 is false.
d We reject H0 and H0 is false.

Q3(0.5 points): What is the level of significance ? Specifically, state what you understand by an value of 0.05 and how it is related to Type 1 error?

Q4 (1.5 points) Provide the information asked for each problem below.
The following statements refer to the alternate hypothesis. In the space provided, in symbolic form write the null and alternate hypothesis.

a. The mean pulse of lawyers is different from 90 beats per minute.
H0: __________________________________________________________________

H1: __________________________________________________________________
b. The mean salary of college presidents is less than $162,500.
H0: __________________________________________________________________

H1: __________________________________________________________________
c. The mean IQ score of 20 year olds is more than 100.
H0: __________________________________________________________________

H1: __________________________________________________________________

Part B
(12 points - all chosen questions carry equal points in this part. There are a total of 5 questions in this part, from which you will choose 4 questions as described further below. )

NOTE FOR Q5 through Q8: In Questions 5 through 8 below, you have to show all 5 steps of the test of hypothesis. Be sure to show your detailed calculations where necessary. Choose any 3 of the questions from Questions 5 through 8 and respond.
Q5. A recent article in a computer magazine suggested that the mean time to fully learn a new software program is 40 hours. A sample of 100 first-time users of a new statistics program revealed the mean time to learn it was 39 hours with the standard deviation of 8 hours. At the 0.05 significance level, can we conclude that users learn the package in less than a mean of 40 hours?
a. State the null and alternate hypotheses.
H0: ____________________________________________________________________
H1: ____________________________________________________________________
b. State the value of alpha. _______________
c. State the test statistic that you will use and why. _______________
d. State the decision rule. _______________
e. Compute the observed value of the test statistic and state your conclusion.
_______________________________________________________________________

Q6. A vinyl siding company claims that the mean time to install siding on a medium-size house is at most 20 hours with a standard deviation of 3.7 hours. A random sample of 40 houses sided in the last three years has a mean installation time of 20.8 hours. At the 0.05 significance level, can a claim be made that it takes longer on average than 20 hours to side a house?
a. State the null and alternate hypotheses.
H0: ____________________________________________________________________
H1: ____________________________________________________________________
b. State the value of alpha. _______________
c. State the test statistic that you will use and why. _______________
d. State the decision rule. _______________
e. Compute the observed value of the test statistic and state your conclusion.
_______________________________________________________________________

Q7. Is the mean salary of accountants who have reached partnership status higher than that for accountants who are not partners? A sample of 15 accountants who have the partnership status showed a mean salary of $82,000 with a standard deviation of $5,500. A sample of 12 accountants who were not partners showed a mean of $78,000 with a standard deviation of $6,500. At the 0.05 significance level can we conclude that accountants at the partnership level earn larger salaries?
a. State the null and alternate hypotheses.
H0: ____________________________________________________________________
H1: ____________________________________________________________________
b. State the value of alpha. _______________
c. State the test statistic that you will use and why. _______________
d. State the decision rule. _______________
e. Compute the observed value of the test statistic and state your conclusion.
_______________________________________________________________________

Q8. The correlation between the number of police on the street and the number of crimes committed, for a sample of 15 comparable sized cities, is 0.45. At the 0.05 significance level is there a positive association in the population between the two variables?

a. State the null and alternate hypotheses.
H0: ____________________________________________________________________
H1: ____________________________________________________________________
b. State the value of alpha. _______________
c. State the test statistic that you will use and why. _______________
d. State the decision rule. _______________
e. Compute the observed value of the test statistic and state your conclusion.
_______________________________________________________________________

NOTE FOR Q9 to Q10: In Question 9 and 10 below, you do not have to do all 5 steps of the test of hypothesis. You are only required to state the hypotheses and the decision rule that you will use to reject the null hypothesis. Note that your decision rule should use the critical value of the test statistic. Choose any 1 of the Questions 9 or 10 and respond.

Q9. The County Executive for Monroe County is concerned about the response time for the three fire companies in the county. Samples of the response times (in minutes) for each company were taken. Each sample size was 5. At the 0.05 significance level is there a difference in the mean response time?

a. State the null and alternate hypotheses.

H0: ____________________________________________________________________

H1: ____________________________________________________________________

b. State the decision rule.

___________________________________________________________________________

Brand Weeks of Wear
Crost 3 4 6 3 4
AQUA 2 3 2 5 2
SONIC 5 7 5 4 6

Q10. A dentist is trying to decide if there is a difference in the number of weeks three different toothbrushes last. A total of fifteen patients were randomly assigned to three brands of toothbrushes and the number of weeks that the toothbrushes lasted is given. At the 0.05 significance level, is there a difference in the mean length of time the toothbrushes lasted?
a. State the null and alternate hypotheses.

H0: ______________________________________________________________________
H1: ______________________________________________________________________

b. State the decision rule.
___________________________________________________________________________