# What is the sampling distribution

1.The main idea underlying all chi-square tests is to compare the observed counts and the expected counts (under ) to each other. (a)True(b)False 2.The direction…

1.The main idea underlying all chi-square tests is to compare the observed counts and the expected counts (under ) to each other.

(a)True(b)False

2.The direction of extreme for a chi-square test of goodness of fit is always one-sided to the left.

(a)True

(b)False

3.In a chi-square test of independence, the degrees of freedom would increase if we increased the sample size.

(a)True

(b)False

4.Fill in the blank. A chi-square test statistic value of –1.8 would imply that _ .

(a)the observed counts are very unlikely and we should reject //<[CDATA[ (function(){window.pagespeed=window.pagespeed||{};var a=window.pagespeed;function b(){}b.prototype.a=function(d,e,c){if(d=document.getElementById(d))if(e=document.getElementById(e))if(c=document.getElementById(c))e.src=d.getAttribute(“src”),c.parentNode.removeChild(c)};b.prototype.inlineImg=b.prototype.a;a.b=function(){a.dedupInlinedImages=new b};a.dedupInlinedImagesInit=a.b;})(); pagespeed.dedupInlinedImagesInit(); //]]>//<[CDATA[ pagespeed.dedupInlinedImages.inlineImg(‘pagespeed_img_2cPQaygk9C1′,’pagespeed_img_2cPQaygk9C2′,’pagespeed_script_3’); //]]>

(b)the observed counts are very unlikely and we should accept //<[CDATA[ pagespeed.dedupInlinedImages.inlineImg(‘pagespeed_img_2cPQaygk9C1′,’pagespeed_img_2cPQaygk9C4′,’pagespeed_script_5’); //]]>

(c)the null hypothesis is false

(d)the alternative hypothesis is false

(e)an error occurred in computing

5.Fill in the blank. The expected counts for a chi-square test should be __ to ensure that the chi-square distribution is the appropriate distribution for //<[CDATA[ pagespeed.dedupInlinedImages.inlineImg(‘pagespeed_img_3JMBwbBsvN6′,’pagespeed_img_3JMBwbBsvN7′,’pagespeed_script_8’); //]]> under the null hypothesis.

(a)at least 5

(b)no more than 5

(c)more than 1

(d)the number does not matter

6.Fill in the blank. The degrees of freedom for a chi-square test of independence when the frequency table has 5 rows and 3 columns is __ .

(a)5

(b)3

(c)15

(d)8

(e)none of the above

7.Fill in the blank. A total of 100 randomly selected new car owners were surveyed and asked to select the primary reason for purchasing their new car from a list of 4 choices. These data were used to assess if there is a significant relationship between gender (male, female) and purchase reason. The appropriate test to conduct is the chi-square test of __.

(a) goodness of fit

(b)homogeneity

(c)independence

8.Fill in the blank. Mr. P. Nut claims to put equal amounts of the different types of nuts in his 20 oz. mixed nuts jars. The jars of mixed nuts contain peanuts, cashews, walnuts, and pecans. To show that his claim holds, he randomly samples some 20 oz. jars off the production line and determines the amount of each type of nut in each jar. The appropriate test to conduct is the chi-square test of .

(a)goodness of fit(b)homogeneity(c)independence

Questions 9 through 13 are based on the following scenario.

A study was conducted to compare two treatments, Treatment I and Treatment II, for heartburn. The 100 subjects were randomly divided into two equal-sized treatment groups. After a 3-month period of using the assigned treatment for heartburn, each subject was asked to rate the effectiveness of the treatment as: highly effective, somewhat effective, or not effective.

9.Which chi-square test is appropriate to compare the effectiveness ratings for the two treatments?

(a) goodness of fit

(b)homogeneity

(c)independence

10.A total of 40 patients rated their treatment as being highly effective. If in fact there is no difference between the two treatments, how many Treatment I subjects would you expect to give a highly effective rating?

11.What is the sampling distribution of the //<[CDATA[ pagespeed.dedupInlinedImages.inlineImg(‘pagespeed_img_3JMBwbBsvN6′,’pagespeed_img_3JMBwbBsvN9′,’pagespeed_script_10’); //]]> test statistic under the null hypothesis that the two treatments are equally effective?

12.Suppose the observed test statistic value is . Report the p-value for the test.

13.Using a 5% significance level, what is your conclusion regarding the effectiveness rates for the two heartburn treatments?