MATH 131 Lab 8
The goal of
this lab is to use the Chi-Square distribution to test a hypothesis.
Chooseeither Plan A
(Goodness of Fit)or Plan B (Independence).
(10
points) PLAN
A: Perform a Chi-Square Test for
Goodness of Fit
According
to Mars, Inc. the distribution of colors in a bag of M&M Plain was 13%
brown, 14% yellow, 13% red, 20% orange, 16% green and 24% blue. Peanut was 12%
brown, 15% yellow, 12% red, 23% orange, 15% green and 23% blue. Dark Chocolate was 17% brown, 17% yellow, 17%
red, 16% orange, 16% green and 17% blue.
·
Purchase
a bag of one of these M&M’s (at least 8 oz.), and record the observed
frequencies for different colors of the candy along with the expected
percentage (Write as a decimal.) for each color.
·
Using
a 5% level of significance (.0/msohtmlclip1/01/clip_image002.gif”>), test the claimed distribution of colors. State the
hypothesis that is being tested. Perform
the Chi Square Test for Goodness of Fit and clearly state your conclusion. Include a sketch as on p. 545 to show your
critical region,.0/msohtmlclip1/01/clip_image004.gif”>, the test statistic, and.0/msohtmlclip1/01/clip_image006.gif”>, the critical value.
(10
points) PLAN
B: Perform a Chi-Square Test for
Independence
Return
to Lab 4 where you made a contingency table with the qualitative variable (V1) and one of quantitative
variables (V2). For
example:
Democrat
Others
Younger
Senators
Older
Senators
·
Find
the row and column sums and compute the expected frequencies for each of the
four cells in the table.
·
Using
a 5% level of significance (.0/msohtmlclip1/01/clip_image002.gif”>), test the two variables for independence. State the
hypothesis that is being tested. Perform
the Chi-Square Independence Test and clearly state your conclusion. Include a sketch to show your critical
region,.0/msohtmlclip1/01/clip_image004.gif”>, the test statistic, and.0/msohtmlclip1/01/clip_image006.gif”>, the critical value.
Minitab
Directions
For Plan B
Enter
the observed frequencies in columns
Select
Stat
Select
Tables
Select
Chi-Square Test
Select
names of the columns containing the observed frequencies
Select
OK
[Minitab
provides the test statistic,P-value
and expected frequencies.]
