1. Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. If all correctanswer positions are equally likely, each would come up approximately 20% of the time. However, it hasbeen speculated that B is the most common correct choice. A random sample of 400 multiple-choicequestions on a variety of AP exams shows that 90 of the 400 questions have B as the correct answer. Doesthis provide evidence that B is the correct choice on more than 20% of all AP exam questions?a. State hypotheses and calculate the sample statistic.b. Are conditions met for using a Normal distribution for this test? Explain. Proceed to answer theremaining steps using a Normal distribution regardless of your answer to this question.c. Calculate the standard error and z-test statistic.d. Use a Normal distribution to find the p-value and draw a curve with appropriate shaded region.Normal curve:p-value:e. State the conclusion of the test in context, using nontechnical language.f. Use Normal distribution methods to find a 95% confidence interval to three decimal places for theproportion of questions on all AP exams having B as the correct choice. Show your calculations.

Sample size (Total number of questions)Number of successes (Correct answer is B)Claim: B is the…

Answered: 1. Multiple-choice questions on…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Is B a Good Choice on a Multiple-Choice Exam?Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400400 multiple-choice questions on a variety of AP exams1 shows that B was the most common correct choice, with 9090 of the 400400 questions having B as the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? Show all details of the test. The data are available in APMultipleChoice. Clearly state the null and alternative hypotheses. Calculate the test statistic and pp-value.Round your answer for the test statistic to two decimal places, and your answer for the pp-value to three decimal places.test statistic == pp-value == Can we conclude that B is more likely to be the correct choice? Yes No
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Are Republicans more likely than Democrats to display the American flag in front of their residence on the Fourth of July? A simple random sample of 618 Republicans were surveyed and 408 said they display the flag on the Fourth of July. Another simple random sample of 615 Democrats were surveyed and 394 said they display the flag on the Fourth of July. Let p1p1 be the proportion of all Republicans who display the American flag on July 4th and p2p2 be the proportion of all Democrats who display the American flag on July 4th. What can be concluded at the αα = 0.10 level of significance? H0:H0: Select an answer μ p1-p2 μ1-μ2 μd p Select an answer ≠ < > = (please enter a decimal) H1:H1: Select an answer μ p1-p2 μd p μ1-μ2 Select an answer ≠ > = < (Please enter a decimal) The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)
Pamela, and educational psychologist, is interested in assessing whether there are differences in how college students with different majors might respond to an ethical dilemma. To this end, she performed a study in which undergraduate marketing and finance majors were asked what they would do if they found a $100 bill in a Walton College of Business classroom. Specifically, would they turn in the $100 bill to the Walton College of Business lost and found? Of the 69 marketing majors who were randomly sampled, 52 said yes and of the 131 finance majors who were randomly sampled, 120 said yes (assume alpha equals .05). z-Test: Two Sample for Means t-Test: Two-Sample Assming Equal Variances Marketing Finance Marketing Finance Меan 0.75362 0.91603 Меan 0.75362 0.91603 Known Variance 0.43 0.28 Variance 0.18841 0.07751 Observations 69 131 Observations 69 131 Hypothesized Mean Difference Pooled Variance 0.1156 -1.7753 Hypothesized Mean DifferenCE z P(Z<-z) one-tail z Critical one-tail P(Z<-z)…
A study considered the question, “Are you a registered voter?” Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 93 people were asked the voter registration question face-to-face. Seventy-nine respondents gave accurate answers. Another random sample of 83 people was asked the same question during a telephone interview. Seventy-four respondents gave accurate answers. Assume that the samples are representative of the general population. Test the claim that there is a difference in the proportion of accurate responses from face-to-face compared with telephone interviews. Use alpha=.05 What is the null hypothesis? What is the alternative hypothesis? What distribution are you using? What test are you running? What is your conclusion?
More than one teacher has given the following advice: choose answer C when blindly guessing among four answers in a multiple choice test, since C is more often the correct answer than either A, B, or D. Suppose that we take a random sample of 600 multiple-choice test answers (the correct answers from the instructor's answer sheet) from introductory college courses and obtain the information summarized by the first row of numbers in the table below. These numbers are the observed frequencies for the categories A, B, C, and D for our sample of 600 correct answers. The second row of numbers contains the frequencies expected for a sample of 600 correct answers if a correct answer is equally likely to be A, B, C, or D. The bottom row of numbers contains the following value for each of the correct answer categories A, B, C, and D. −fOfE2 fE = −Observed frequencyExpected frequency2 Expected frequency
A political scientist claims that 38% of first-year college students characterize themselves as being “moderate” or “middle of the road” as far as their political affiliation is concerned. Believing this claimed value is too high, you survey a random sample of 400 first-year college students and find that 120 characterize themselves as being “moderate” or “middle of the road.” Based on this information, what will the test statistic be? Choose the answer below that is closest to what you calculate, and try not to do a lot of rounding until you get to the very end of your calculations. 1. -0.3 2. -1.2 3. -2.6 4. -3.3 5. None of the other answer options are correct because the test statistic should be positive, not negative.
A salesman makes initial telephone contact with potential customers in an effort to assess whether a follow-up visit to their homes is likely to be worthwhile. His experience suggests that 40% of the initial contacts lead to follow-up visits. Suppose he contacts 100 people by telephone and the sample proportion of the follow-up visit is calculated. Which of the following statements is (are) correct? This is a multiple-answer question. It may have more than one correct answers. i. The sample proportion has a normal distribution with a mean of 0.40 and a standard deviation of 04x0.4 = 0.049. 100 Oil. The sample proportion has a normal distribution with a mean of 0.40 and a standard deviation of 0.6. iii. The probability that the sample proportion of the follow-up visit is more than 50% is P(p>0.5) = P(z>04-05)=P(z>-2.04) = 1-0.0207 = 0.9793. iv. The probability that the sample proportion of the follow-up visit is more than 50% is P(p>0.5)=P(2> 05 = P(Z > 2.04) = 1-0.9793= 0.0207.…
A high school track coach wanted to test whether giving the students an energy drink could affect performance during the 100 meter race. The coach split the 26 boys into two equal sized groups, where Group 1 was given the energy drink and Group 2 was not. The 100 meter race times were recorded during practice and shown in the table below. What inference can be made about the results? Group 1 Group 2 12.2 13 12.5 12.3 13.3 12.8 12.9 13 13 13.8 12.1 13 13 13 13 13 12.1 13 13 13 12.1 13 12.8 13 13 12.6 Mean: 12.7 Mean: 13 Since the simulation shows ( many cases or free cases )? where a mean difference of ( solve for this answer ) or less occurred when the groups were re-randomized, it can be inferred that the mean difference observed in the study was ( very possibly or very unlikely ) ?due to the random assignment of participants into groups, so the results of the study are (…
A research paper describes an experiment in which 74 men were assigned at random to one of four treatments. 1. viewed slides of fit, muscular men 2. viewed slides of fit, muscular men accompanied by diet and fitness-related text 3. viewed slides of fit, muscular men accompanied by text not related to diet and fitness 4. did not view any slides The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the following table. Treatment 1 9 6 4 13 1 2 5 9 12 5 2 0 7 4 10 6 0 11 Treatment 2 Treatment 3 7 8 0 3 9 8 7 1 6 8 8 5 13 9 0 7 4 11 5 7 10 8 7 1 10 2 5 1 0 3 0 3 4 4 5 5 6 8 4 0 7 3 Treatment 4 5 2 5 7 5 2 0 0 4 3 2 3 1 1 Do these data provide convincing evidence that the means for the numbers of pretzels consumed are not the same for…
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