Testing of hypothesis

(See attached file for full problem description)

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The lives of many people are affected by fear that prevents them from flying. The Marist Institute of Public Opinion conducted a poll of 1014 adults, 48% of whom were men. According to a USA Today newspaper poll.

? 47% of Adults believe flying is the safest way to travel and 22% do not believe flying is the safest way to travel
? 39% believe cars are the safest way to travel
? 14% believe trains are the safest way to travel
? About 41 million Americans are afraid
? 12% of men and 33% of women fear flying

Analyzing the Results:

1) Is there sufficient evidence to conclude that there is significant difference between the percentage of men and the percentage of women who hear flying?
SOLUTION

Yes , there is significant difference between men and women who fear flying.(this answer is incomplete needs a little more explanation I think)

2) Construct a 95% confidence interval estimate of the difference between the percentage of men and the percentage of women who fear flying. Do the confidence interval limits contain 0, and what is the significance of whether they do or do not? (I need to answer the question about the significance of 0 and not sure how to do it)

SOLUTION

Here n=1014 and p=0.33-0.12=0.21
Hence x/ = np = 212.94

For 95 percent confidence interval zα/2 = 1.96
S = √(npq)
= √(212.94*0.21*0.79)
=5.9436
The required interval is :

212.94 - (1.96) (5.9436)/&#8730; (1014) < µ < 212.94 + (1.96) (5.9436)/&#8730; (1014)

212.57 < µ <213.30
3) Construct a 95% confidence interval for the percentage of men who fear flying.

SOLUTION

Men=1014*0.48=486.72
Here n=486.72 and p=0.12
Hence x/ = np = 58.40
For 95 percent confidence interval z&#945;/2 = 1.96

S = &#8730;(npq)
= &#8730;(486.72*0.12*0.88)
=7.169

The required interval is :

58.40 - (1.96) (7.169)/&#8730; (486.72) < µ < 58.40 + (1.96) (7.169)/&#8730; (486.72)
57.76<µ<59.03

4) Based on the result from Exercise #3, complete the following statement, which is typical of the statement that would be reported in a news paper or magazine: "Based on the Marist Institute for Public Opinion poll, the percentage of men who fear flying is 22% with a margin of error of ________."

SOLUTION

+ 10. (not sure if margin of error is correct)

5) Examine the completed statement in exercise #4. What important piece of information should be included, but is not included?

SOLUTION

The sample size 1014 and percentages of men and women must be included.

6) In a separate Gallup poll, 1001 randomly selected adults were asked this question: "If you had to fly on an airplane tomorrow, how would you describe your feelings about flying? Would you be----very afraid, somewhat afraid, not very afraid, or not afraid at all? Here are the responses:
? Very afraid 18%
? Somewhat afraid 26%
? Not very afraid 17%
? Not afraid at all 38%
? No opinion 1%

Are these Gallup poll results consistent with those obtained by the survey conducted by the Marist institute for Public Opinion? Explain. Can discrepancies be explained by the fact that the Gallup survey was conducted after the terrorist attacks of September 11, 2001, whereas the other survey was conducted before the date?

SOLUTION

Gallup poll results are not consistent with those obtained by the survey conducted by Marist institute for Public opinion. Yes terrorist attacks of September 11, 2001 could be the major reason because air travel greatly decreased after the incident largely due to fear.

7) Does the USA today paper do a good job o depicting survey results? Construct a graph which more clearly illustrates the survey results.

SOLUTION

USA today paper depicting survey results should have margin of error listed.

Here is the data and graph of the current survey: About 41 million adults are afraid to fly. Percent of Americans who fear flying, margin of error =/- 10 percent.

1 Very afraid 18%
2 Somewhat afraid 26%
3 Not very afraid 17%
4 Not afraid at all 38%
5 No opinion 1%