In a survey of 500 likely voters, 271 responded that they would
vote for the incumbent and 229 responded that they would vote for
the challenger. Let pp denote the fraction of all likely voters who
preferred the incumbent at the time of the survey, and let p^p^ be
the fraction of survey respondents who preferred the
incumbent.
a. Use the survey results to calculate p^p^.
b. Test the hypothesis H0:p=0.5 vs. Ha:p≠0.5H0:p=0.5 vs. Ha:p≠0.5
at the 5% significance level. Remember to state your assumptions.
Keep in mind that you should calculate the standard error
assuming the null hypothesis is true. This means
that you should use pp in your standard error calculations.
c. What is the p-value for the test H0:p=0.5 vs.
Ha:p≠0.5H0:p=0.5 vs. Ha:p≠0.5? [Note: Unfortunately, the letter "p"
is used both to denote a probability and a proportion. When we
write/say p-value, we mean a probability, in this case,
the probability that the null is true. When we
write/say H0:p=0.5H0:p=0.5, we mean the null hypothesis that the
population proportion is 0.5.]
d. What is the p-value for the test H0:p=0.5 vs.
Ha:p>0.5H0:p=0.5 vs. Ha:p>0.5?
e. Do the results from (c) to (d) differ? Why or why not?
f. Did the survey contain statistically significant evidence that
the incumbent was ahead of the challenger at the time of the
survey? Explain.
g. Suppose you knew (you are now omniscient) that the fraction of
all likely voters who preferred the incumbent at the time of the
survey was p=0.5p=0.5. You would like to do a survey of all likely
voters, but can only conduct a survey on landlines, i.e. cell
phones are not included. A survey using a simple random sample of
500 landline telephone numbers finds that 54% of respondents
support the incumbent. Is there evidence that the survey is biased?
Explain.
h. A survey using a simple random sample of 500 landline telephone
numbers finds that 55% of respondents support the incumbent. Is
there evidence that the survey is biased? Explain. Compare to part
(g) and explain any similarities and differences in
conclusions.
i. For a sample of 500, what proportion of respondents that support
the incumbent should there be to not worry about bias?
here since n is very large therefore we will apply z statistic to perform testing of our null hypothesis, which is. e) the result from c and d are different because in part c we apply z test for two tailed and for d part we apply single or one tail or right tailed t test.
f) this is the language term of part d. here we have seen in part d that we reject null hypothesis that p=0.5 that is p=q, against p>0.5, therefore survey contain statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey.
In a survey of 500 likely voters, 271 responded that they would vote for the incumbent...
In a survey of 500 likely voters, 271 responded that they would vote for the incumbent and 229 responded that they would vote for the challenger. Let pp denote the fraction of all likely voters who preferred the incumbent at the time of the survey, and let p^p^ be the fraction of survey respondents who preferred the incumbent. a. Construct a 95% confidence interval for pp. Keep in mind that you should calculate the standard error making no assumptions of...
20 pts] In a survey of 400 likely voters, 215 responded that they would vote for the incumbent and 185 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent. (g) Construct a 95% confidence interval for p. (h) Construct a 99% confidence interval for p. (i) Why is the...
(2) 120 pts] In a survey of 400 likely voters, 215 responded that they would vote for the incumbent and 185 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at the time of the survey, and let p be the fraction of survey respondents who preferred the incumbent. (a) Use the survey results to estimate p. (b) Use the estimator of the variance of p, p(1 -p)/n,...
show your workings In a survey of 400 likely voters, 213 responded that they would vote for the incumbent and 187 responded that they would vote for the challenger. Let p denote the fraction of all likely voters who preferred the incumbent at the time of the survey, and lot be the fraction of survey respondents who preferred the incumbent. Using the survey to the estimated value of pis 0.5325. Round your response to four decimal places.) Using Pt-pyn as...
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We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.04 at 95% confidence? Use a planning value of p∗= 0.5. a. 601 b. 600 c. 385 d. 307
Only 14% ofregistered voters voted in the last election will voter participation change for the upcoming election? Of the 369 randomly selected registered voters surveyed, 63 of them will vote in the upcoming election. What can be concluded at the α-0.01 level of significance? a. For this study, what sampling distribution would be used? Select an answer b-The null and alternative hypotheses would be: (please enter a decimal) Hİ : [pvi-[ (Please enter a decimal) c. The test statistic? d....
year, a survey was c indicated that they would vote for the incumbent. This month, Victoria C mayor. to determine the degree of support for the Mayor of New Orleans. of a random sample of 1,242 voters ithe New Oleanseea 54% hustz took a random sample of 1,218 voters in the same area and found that only 42%of them ร pport the 1. Last year 2. This sonth 1,218 Can we infer that the mayor's popularity has decreased by (i)...
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