STAT200 week 8 homework

STAT-200 Homework Assignments Week #8

Textbook #1: Lane et al. Introduction to Statistics, David M. Lane et al., 2013.
(http://onlinestatbook.com/Online_Statistics_Education.pdf )

Textbook #2:Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013.

(http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562-op.pdf )

Lane - Chapter 15: (1,5,8,10)

1. What is the null hypothesis tested by analysis of variance?

5. What is the difference between “N” and “n”?

8. What kind of skew does the F distribution have?

10. Assume an experiment is conducted with 5 conditions and 6 subjects in each condition.

What are df_numerator and df_denominator?

Illowsky – Chapter 13 (61,63,69,71,77,81)

HINT: In order to create an ANOVA table, you will need to follow examples 13.1 and 13.2 in your book. At the end of this homework assignment, there is also another detailed example. DO NOT calculate the SS_within by hand. Use EXCEL (or calculate by hand) the value for SS_totaland then calculate the value for SS_between. The value of SS_within = SS_total – SS_between. Use the equations in the summary table at the top of page 699 to find the value of the F-statistic and then find the P-value.

Use the following information to answer #61 and #63. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

Null-Hypothesis is H₀: ?1 = ?2 = ?3 = ?4 = ?5

Alternate Hypothesis is H_?: At least any two of the group means ?1, ?2, …, ?5 are not equal.

61. Find the degrees of freedom (numerator) = df(num)

63. Find the F-statistic using an ANOVA table.

69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. The table (on right) shows the results of a study. Assume that all distributions are normal, the population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? The table (on right) shows the results of a study. Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows (see table). Determine whether or not the variance in mileage driven is statistically the same among the groups. Use a 5% significance level.

81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? The table (on right) shows the results of a study. Assume a 10% significance level.

HINT: See Section 13.4 (Test of Two Variances) to find the F-statistic. Assume the null hypothesis is the variances are the same and assume the alternate hypothesis is.

Example: Calculations in the Analysis of Variance (ANOVA)

Example Solution Table

P-value using F-distribution (use EXCEL formula)

FDIST (F, df1, df2) = FDIST(9.085,4,45) = 0.00001815