Problem 1) Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals. To test this hypothesis, she has two assistants sit in a McDonalds restaurant and identify individuals who order the Big Mac special for lunch. The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight. The assistants identify 10 overweight and 10 normal weight Big Mackers. The assistants record the amount of time it takes them to eat the Big Mac special.

1.0 585.0
1.0 540.0
1.0 660.0
1.0 571.0
1.0 584.0
1.0 653.0
1.0 574.0
1.0 569.0
1.0 619.0
1.0 535.0
2.0 697.0
2.0 782.0
2.0 587.0
2.0 675.0
2.0 635.0
2.0 672.0
2.0 606.0
2.0 789.0
2.0 806.0
2.0 600.0

a) Compute an independent-samples t-test on these data. Report the t-value and the p values. Were the results significant? (Do the same thing you did for the t-test above, only this time when you go to compare means, click on independent samples t-test. When you enter group variable into grouping variable area, it will ask you to define the variables. Click define groups and place the number 1 into 1 and the number 2 into 2).

b) What is the difference between the mean of the two groups? What is the difference in the standard deviation?

c) What is the null and alternative hypothesis? Do the data results lead you to reject or fail to reject the null hypothesis?

d) What do the results tell you?

Problem 2)Lilly collects data on a sample of 40 high school students to evaluate whether the proportion of female high school students who take advanced math courses in high school varies depending upon whether they have been raised primarily by their father or by both their mother and their father. Two variables are found below in the data file: math (0 = no advanced math and 1 = some advanced math) and Parent (1= primarily father and 2 = father and mother).

Parent Math
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
2.0 0.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0

a) Conduct a crosstabs analysis to examine the proportion of female high school students who take advanced math courses is different for different levels of the parent variable.

b) What percent female students took advanced math class

c) What percent of female students did not take advanced math class when females were raised by just their father?

d) What are the Chi-square results? What are the expected and the observed results that were found? Are they results of the Chi-Square significant? What do the results mean?

e) What were your null and alternative hypotheses? Did the results lead you to reject or fail to reject the null and why?

Problem 3) This problem will introduce the learner into a technique called Analysis of Variance. For this course we will only conduct a simple One-Way ANOVA and touch briefly on the important elements of this technique. The One-Way ANOVA is an extension of the independent t test that can only look at two independent sample means. We can use the One-Way ANOVA to look at three or more independent sample means. Use the following data to conduct a One-Way ANOVA:

Scores Group
1 1
2 1
3 1
2 2
3 2
4 2
4 3
5 3
6 3

Notice the group (grouping) variable, which is the independent variable or factor is made up of three different groups. The scores are the dependent variable.

Use the instructions for conduction an ANOVA on page 366 of the text for SPSS or Excel.

a) What is the F-score; Are the results significant, and if so, at what level (P-value)?

b) If the results are significant to the following: Click analyze, then click Compare Means, and then select one-way ANOVA like you did previously. Now click Post Hoc. In this area check Tukey. If there is a significant result, we really do not know where it is. Is it between group 1 and 2, 1 and 3, or 2 and 3? Post hoc tests let us isolate where the level of significance was. So if the results come back significant, conduct the post hoc test as I mentioned above and explain where the results were significant.

c) What do the results obtain from the test mean?