The Future: Are Things Getting Better or Worse? To test and see what Americans t

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The Future: Are Things Getting Better or Worse? To test and see what Americans think about the future, go to Polling Report. Under NBC News/Wall Street Journal Poll conducted by Hart Research Associates, consider the results to the question: "Do you feel confident or not confident that life for our children's generation will be better than it has been for us?" Are Americans more pessimistic about the future than they were ten years ago?
1. Run a hypothesis test to see if the percentage of people in 2014 that responded "not confident" has increased significantly since 1993. Note that it states on the website that the samples are of size 500. Use alpha = .05 Run the test using the Test Statistic / Critical
Value approach. Set up the null and alternative hypotheses and Show all your work. Make sure to explain what the test results tell you in the context of the problem. 2. Why or why not are you surprised by these results? 3. What is the p-value? Run the test using the p-value / level of significance approach. 4. What is the population being studied in this test? 5. What are the population parameters that are being measured? 6. What cautions may there in using survey (polling data) such as this?

NBC News/Wall Street Journal Poll conducted by Hart Research Associates (D) and Public Opinion Strategies (R). July 30-Aug. 3, 2014. N=approx. 500 adults nationwide.

"Do you feel confident or not confident that life for our children's generation will be better than it has been for us?"

7/30 - 8/3/14

5/16-20/12

8/26-/30/10

12/11-14/09

6/12-15/09

9/19-22/08 RV

12/14-17/07

1/07

7/06

12/01

9/93

12/92

"Do you feel confident or not confident that life for our children's generation will be better than it has been for us?"

Confident Not
confident Unsure % % %

7/30 - 8/3/14

21 76 3

5/16-20/12

30 63 7

8/26-/30/10

27 66 7

12/11-14/09

27 66 7

6/12-15/09

31 57 12

9/19-22/08 RV

35 56 10

12/14-17/07

30 64 6

1/07

33 60 7

7/06

27 65 8

12/01

49 42 9

9/93

25 68 7

12/92

41 52 7

Explanation / Answer

We used z-proportion test.

(1)

(2) Yes, we are surprised with the result. It concludes that American becoming pessimistic about the betterment of young generation.

(3)

Formula in excel:

=1-NORM.S.DIST(2.82,TRUE)

Still the conclusion remains same since p-value<0.05, we reject H0.

(4) Population is hypothetical as in all Americans. However, just 500 samples are considered for study.

(5) Population parameters being measured is "percentage of people that responded "not confident".

(6) Cautions:

1. Avoid biasness in sampling

2. samples must be iid

3. Right sampling technique

Period 1993 2014 proportion of not-confident 68% 76% p1 p2 sample size 500 500 n1 n2 H0: p2<=p1 Ha: p2>p1 Assumption: binomial approximation to Normal point estimate=p2-p1= 8% pooled proportion p= (n1p1+n2p2)/(n1+n2) 72% pooled SD=SQRT(P*(1-P)) 0.448999 Std Error= SD*SQRT(1/n1+1/n2) 0.028397 test stat z= point estimate/Std Error 2.817181 Z_critical at 5% level= 1.644854 Since z_obsereved > z_critical, so reject H0; conclude that yes, the proportion has increased significantly.

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