UNIVERSITY OF MINNESOTA, MORRIS

INTRODUCTION TO STATISTICS

(GENED WEB)

MATH. 1601

SOLUTIONS TO THE PRACTICE TEST

SUMMER, 1999

FOR INSTRUCTOR'S USE

1.	........../5
2.	........../5
3.	........../5
4.	........../5
5.	........../5
TOTAL	........../25

Question 1.

(5 Points) The May 13-17 1999 Program on International Policy Attitudes polled 1206 adults in the USA, and asked "Do you think NATO made the right decision or the wrong decision by starting the airstrikes against Yugoslavia?". Suppose approximately 51 percent of the respondents said they made the wrong decision. Does this survey provide evidence that a majority of USA adults think NATO made the wrong decision?

Do a hypothesis test to address this question.

Let p=the proportion of USA adults who think NATO made the wrong decision.

H₀: p=0.50

H_a: p>0.50

z=(0.51-0.50)/Squarerootof(0.50x0.50/1206)=0.01/0.0144=0.69

p-value=P(z>0.69)=1-0.7549=0.2451

Since p-value is large, we do not have enough evidence to reject the null hypothesis. Therefore, we can not conclude that majority of USA adults think NATO made the wrong decision.

Question 2.

(5 points) Insect traps of two colors (white, green) were placed in a small grain field. The numbers of bugs caught in the white traps are given below followed by the number in the green traps.

Numbers of bugs caught in white traps: 21 12 14 17 13 17

Numbers of bugs caught in green traps: 37 32 15 25 39 41

Some Summary Statistics:


	N	MEAN	STANDART DEVIATION
white	6	15.67	3.33
green	6	31.50	9.91

Is there evidence that there is a difference in the effectiveness of the traps to catch bugs? Use a hypothesis test to address this question. Give all steps and reasoning.

Let m₁ =population mean for white

m₂=population mean for green

H₀: m₁- m2=0

H_a: m₁- m₂=/ 0

t=(15.67-31.50)/SquareRootof(3.33²/6+9.91²/6)

=-15.83/4.263=-3.70

d.f.=5

0.005<p-value<0.01

Therefore at a=0.05 significance level we have enough evidence that there is a difference in the effectiveness of the traps to catch bugs.

(Note: you may also use the pooled two-sample t procedure)

Question 3.

(5 points) A recent Gallup Poll found that 47 percent of 761 respondents had a favorable impression of the National Rifle Association. In a May 1995 study of 743 respondents it was found that 44 percent of respondents had a favorable impression of the NRA. Has the favorable impression proportion changed from 1995 to today?

Perform a confidence interval to address this question. Provide all steps, and a complete conclusion.

Let p₁=population proportion for today and p₂=population proportion for 1995

A 95% confidence interval for (p₁- p₂) is

(0.47-0.44)+-1.96xSE_D

0.03+-1.96x0.02567

0.03+-0.05

(-0.02,0.08).

Since 0 is in this interval, at 95% confidence level we can not conclude that there is a change of opinion from 1995 to today on the impression of NRA.

Question 4.

(5 Points) A survey called the Health Examination Survey were asked "Have you ever felt you were going to have a nervous breakdown?" The results for men aged 25 to 34 showed that out of 543 married men, 40 answered yes. For a total of 99 never married men, 9 answered yes. Is there evidence of a relationship between marital status and their answer to the mental health question?

Use a hypothesis test to address this question. You must provide a clear and complete conclusion.

	Married?
Stress?	Yes	No	TOTAL
Yes	40(41.44)	503(501.56)	543
No	9(7.56)	90(91.44)	99
TOTAL	49	593	642

Expected counts are given in parentheses.

ChiSq = X² = 0.050 + 0.004 + 0.276 + 0.023 = 0.353

df = 1

p-value>0.25

There is no evidence of a relationship between marital status and their answer to the mental health question.

(Note: you can also formulate the solution as a difference between proportion)

Question 5.

(5 Points) The Western Electric Longitudinal Study produced the following data regarding coronary heart disease (CHD) and work environment.
	Major CHD Event
Do You Work Under Tension?	Yes	No	TOTAL
Yes	97	307	404
No	200	1409	1609
TOTAL	297	1716	2013
Use these data to determine if there is evidence for a relationship between workplace stress and a coronary heart disease event. Use a contingency table approach with a chi-squared test statistic in your hypothesis test. Give a complete conclusion in addition to all the steps in the test.

H₀: no relationship between stress and CHD

H_a: relationship between stress and CHD

TABLE OF EXPECTED CELL COUNTS

	Major CHD Event
Do You Work Under Tension?	Yes	No	TOTAL
Yes	59.61	344.39	404
No	237.39	1371.61	1609
TOTAL	297	1716	2013

ChiSq =X²= 23.458 + 4.060 + 5.890 + 1.019 = 34.428

df = 1

p-value<0.0005 (Table F.)

We reject the null hypothesis. There is a strong evidence for a relationship between workplace stress and a coronary heart disease event.