Math 146 – Introductory Statistics – Spring 2015
Quiz Chap 10
Name: __________________________________
1. (2 pt) True or False
a) The chi squared test for independence is always one-tailed; the chi-square test of Goodness-of-Fit is
always two-tailed. False
b) A chi-squared distribution is used to test whether a frequency distribution fits an expected
distribution. True
c) If the test statistic for the chi-square independence test is small, you will, in most cases, reject the
null hypothesis. False
d) If the two variables in a chi-square test for independence are independent, then you can expect little
difference between the observed frequencies and the expected frequencies. True
2. (1 pt) What conditions are necessary to us a chi-square Goodness-of-Fit test?
-random samplew
- each E must be at least 5
3. (1 pt) Find the expected frequency for the given values of n and pi.
n= 21 pi = .7
.7*21 = 14.7
4. (1 pt) A researcher claims that the number of different colored candies in a bag of M&M’s is
uniformly distributed. A sample of 120 M&M’s is randomly selected. There are 6 possible colors
of M&Ms.
What is the Expected number of red M&M’s?
120/6 = 20
5. (2 pt) The results of a random sample of patients with a slubby disorder is shown in the table.
One claims that slubby disorder is related to gender.
a) Give the hypotheses one would use to test this claim.
H0 : slubby disorder and gender are independent
Ha : slubby disorder and gender are dependent
b) What is the expected value of a male with the slubby disorder?
Has slubby
disorder
4
8
Female
Male
No slubby
disorder
6
2
12*10/20 = 6
5. (1 pt) In a test for equal variances:
α = 0.05
dfN =9
dfD= 16
a) Give the critical value 3.05
b) Define rejection region in terms of critical value
6. (2 pt) The annual salaries for a random sample of 17 actuaries working in California have a
standard deviation of $9600. The annual salary for a random sample of 16 actuaries working
in New York have a standard deviation of $14900. One claims that the standard deviation of
annual salaries is greater in California than it is in New York.
a) Give the hypotheses one would use to test the claim.
H0 : σ1 ≤ σ2
Ha : σ1 > σ2
b) Give the test statistic (an expression, do not simplify!!), and degrees of freedom (be specific) one
would use to test the claim.
𝑭=
dfN = 15
dfD = 16
𝟏𝟒𝟗𝟎𝟎𝟐
𝟗𝟔𝟎𝟎𝟐