Question

In: Statistics and Probability

In a random sample of 60 voters, 34 reported they voted for Candidate A and 26...

In a random sample of 60 voters, 34 reported they voted for Candidate A and 26 reported they voted for Candidate B. Let G denote a random variable equal 1 if the person voted for A and 0 if the person voted for B.


(a) Find the sample average, ¯ G, and sample variance, S^2 G, of variable G.
(b) Does Candidate A have more than 50% of the popular vote? Formulate and test the corresponding null and alternative hypotheses to answer this question, interpret results.

(c) Are Candidates A and B virtually tied? Formulate and test the corresponding null and alternative hypotheses to answer this questions, interpret results.

Solutions

Expert Solution


Related Solutions

Suppose that 60% of registered voters support candidate A. A pollster will obtain a random sample...
Suppose that 60% of registered voters support candidate A. A pollster will obtain a random sample of 200 registered voters. What is the probability that at least 126 of the individuals in the sample support A? Do not employ a continuity correction. 0.8078 0.2447 0.1922 0.0749 0.5956
In a random sample of 750 voters exiting Dallas polls, 450 claimed to have voted for...
In a random sample of 750 voters exiting Dallas polls, 450 claimed to have voted for the constitutional amendment banning marriage for two individuals of the same sex. Construct a 99% confidence interval estimate of the proportion of votes for this constitutional amendment in Dallas. A. 57% - 63% B. 55% - 65% C. 56% - 64% D. None of the above
To check whether the popularity of a political candidate is down from 60%, a random sample...
To check whether the popularity of a political candidate is down from 60%, a random sample of 1000 voters is surveyed. K out of 1000 favor the candidate. If K=580 test the 60% popularity hypothesis at significance level α = .05. Find the minimal number K that does not reject the 60% popularity hypothesis. Using Ti-34 calculator Equations/answer written out using binomcdf(x,x,x) Binompdf(x,x,x) Invnorm InvT tcdf If possible/needed to solve the equation
A sample of 500 male registered voters showed that 57% of them voted in the last...
A sample of 500 male registered voters showed that 57% of them voted in the last presidential election. Another sample of 400 female registered voters showed that 55% of them voted in the same election. a. Construct a 97% confidence interval for the difference between the proportions of all male and all female registered voters who voted in the last presidential election. b. Test at the 1% significance level whether the proportion of all male voters who voted in the...
A random sample of BMI from college students were collected as follows: 23 32 34 26...
A random sample of BMI from college students were collected as follows: 23 32 34 26 23 28 38 33 25 29 28 Find sample size. Find sample median. Find sample mean. Find IQR. Construct a box plot. Mention one reason that box plot is useful What aspect of the data are both the sample standard deviation and IQR measuring? List an advantage and disadvantage of each. If each person’s BMI in the sample increase the same amount, 5, how...
In a random sample of 50 voters, intended to show that more voters are in favor...
In a random sample of 50 voters, intended to show that more voters are in favor of candidate A, 34 said they favor candidate A. (a) What is the probability that this many or more voters would favor A is the true proportion of all eligible voters favoring A is 0.54? (b) Is the result significant at the 0.05 level? What about the 0.01 level? Explain your answers.
15. In a random sample of 60 adults, 55% of them reported having a fear of...
15. In a random sample of 60 adults, 55% of them reported having a fear of public speaking. (1)(1.5 points) Are the assumptions for constructing a confidence interval for the population proportion satisfied? Explain. (2)(5 points) Construct a 99% confidence interval for the population proportion of adults who have a fear of public speaking. (3)(2.5 points) Interpret the 99% confident interval. (4)(3.5 points) Estimate the sample size needed so that a 99% confidence interval will have a margin of error...
it has been reported that 48% of people text and drive. A random sample of 60...
it has been reported that 48% of people text and drive. A random sample of 60 drivers is drawn. Find the probability that the proportion of people in the sample who text and drive is less than 0.498.
In a recent election, 36% of registered voters actually voted. Assuming the population proportion of voters...
In a recent election, 36% of registered voters actually voted. Assuming the population proportion of voters is 36%, find the probability that in a random sample of 75 people less than 40% will vote. Round off your answer to four decimal places.
A sample poll of 100 voters chosen at random from all voters in a given school...
A sample poll of 100 voters chosen at random from all voters in a given school district indicated that 53% of them were in favor of a 1% increase in property taxes in order to provide funds to hire more teachers.           a.       Find the 95% confidence interval for the population proportion of voters supporting the property tax                     hike?           b.       Can we be confident that the tax hike will pass given your results in part (a)? Explain....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT