ㅇㅁSmart Driver Driving School has many branches across provinces. In a province different from the one in problem 1, the teaching committee atthe provincial branch randomly assigned half of their 5000 students enrolled this year to receive the conventional teaching method and the remaining halfto receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 78 passed the road test. Inanother random sample of 100 students who received the new teaching method, 84 passed the road test. The committee would like to use the sampledata to test if the two teaching methods have different passing rates. Let pc and py be the true passing rates of the conventional and the new teachingmethods, respectively.Part i) What are the appropriate null and alternative hypotheses?OA. Ho: Pc PN = 0 and HAOB. Ho: Pc.- PN = 0 and HAPC - PN <0PC - PN0OC. Ho: Pc - PN = 0 and HAPC - PN0OD. Ho PN = 0.78 and HA PN 0.78Part ii) The committee decides to perform the hypothesis test at 10% significance level. Which of the following is/are true? (Check all that apply.)A. The Type Il error is 90%.B. There is 10% chance to reject the null hypothesis.C. The Type I error is 10%.D. The probability of committing the Type I error is 10%.OE. There is 10% chance that the null hypothesis is true.OF. The probability of committing the Type II error is 90%.G. None of the above.Part iii) Which of the following assumptions and conditions are needed to carry out the hypothesis test? CHECK ALL THAT APPLY.A. The population sizes are sufficiently large.OB. The two random samples are no larger than 10% of their respective population sizes.OC. The two random samples of students are independent.D. The variable whether a student passes or not follows the Normal model.DE. None of the above.Part iv) Construct a 95% confidence interval for the difference in the true passing rates (expressed as proportions) between the conventional and newteaching methods:95% confidence interval: ( -0.1578 0.0578 [Your two numbers must be rounded to 3 decimal places. Keep at least 6 significant figures inintermediate steps.]

Given, For Conventional teaching method: sample size (n1) = 100 x1 = 78 sample proportion (p1^) =…

Answered: branch randomly assigned half of their…

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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A sports enthusiast would like to determine if the average number of penalty minutes per game for teams in the National Hockey League is greater than 12 minutes. A sample of 30 games was taken, and the number of penalty minutes in each game was recorded. Select the appropriate hypotheses to be tested. Ho:μ=12Ho:μ=12Ha:μ>12Ha:μ>12 Ho:μ=12Ho:μ=12Ha:μ≠12Ha:μ≠12 Ho:¯y=12Ho:y¯=12Ha:¯y≠12Ha:y¯≠12 Ho:¯y=12Ho:y¯=12Ha:¯y>12
QUESTION 12 Suppose we are interested in whether travelers departing to Bali have spent researching potential health risks. Let the population proportion be denoted by p and assume we are interested in testing whether there is evidence that more than 40% of travelers have researched potential health risks. Which of the following represents the correct set of hypotheses for this 1-tailed test? O a. Ho: 0 = 0.4 H: р 0.4 O d. Ho: p = 0.4 H1: p> 0.4
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
60% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 130 of the 241 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of a = 0.01? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho:1?v Но: 7Select an answer v (please enter a decimal) H1:1?v|Select an answer v (Please enter a decimal) c. The test statistic ? (please show your answer to 3 decimal places.) d. The p-value (Please show your answer to 4 decimal places.) e. The p-value is ? va f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusiion is that .. The data suggest the population proportion is not significantly smaller than 60% at a = 0.01, so there is not sufficient evidence to conclude that the population proportion of students who played intramural sports who received…
Imagine you are doing a Related-Samples t-test, and you are on Step Two of the hypothesis test. The sample of difference scores that you calculated is -1, -1, -3, +2, 0, -4. If you are doing the test with α = .01, and two tails, what would he correct t-critical be?
Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 383 patients who received the antidepressant drug, 122 were not smoking one year later. Of the 617 patients who received the placebo, 106 were not smoking one year later. Given the null hypothesis H0: (pdrug−pplacebo)=0 and the alternative hypothesis Ha: (pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.05, (a) The test statistic is (b) The P-value is (c) The final conclusion is A. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group. B. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.
1. The incidence of cancer among phosphate mine workers and their exposure to radiation was investigated. Cancer incidence was recorded among 60 phosphate mine workers who had 0-29 working level months (WLM) of exposure, 60 phosphate mine workers who had 30-89 WLM of exposure, and 60 phosphate mine workers who had 90-120 WLM of exposure. The number of cancer incidences for each group are presented in Table 1. Table 1: Two-way Table of Counts Cancer Incidence Exposure Level Yes No Total 0-29 WLM 20 40 60 30-89 WLM 33 27 60 90-120 WLM 43 17 60 Total 96 84 180 Perform a x? test, at the 5% level of significance, whether cancer incidence rates differ between the three levels of radiation among phosphate mine workers.
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Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 118 patients who received the antidepressant drug, 51 were not smoking one year later. Of the 882 patients who received the placebo, 319 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.02, (a) The test statistic is (b) The P-value is
In a random sample of 80 male students at a college, 28 said they frequently send at least one text message before getting out of bed in the morning. In a random sample of 105 female students at the same college, 50 said they frequently texted before getting out of bed. Let p₁= the proportion of all male students at this college who frequently text before getting up, and let p2= the corresponding proportion for female students. For a test of the hypothesis Ho: p₁-P2 = 0, which of the following is a correct expression for the test statistic? a. 0.35 -0.48 0.48(0.52) 0.35(0.65) 80 + 105 b. 0.350.48 0.35(0.65) 0.48(0.52) + 80 105 (0.42)(0.58) 185 Z=
Normally only about 19% of people who try to quit smoking succeed, but sellers of a motivational tape claim that listening to their recorded messages can help people quit (i.e., more than 19% of the people who use the tapes will successfully quit). Let p represents the percentage of people who have listened to the recorded messages and have successfully quit. Match the appropriate null and alternative hypotheses, based on the sellers' claim. H,: p = 0.19 p> 0.19 p2 0.19 ps 0.19 p 0.19 p2 0.19 ps 0.19 p < 0.19 Op- 0.19 Do you consider a Type I or Type Il error a more serious mistake here? Why? Your answer should make it clear what Type I and Il errors are in this context.
Suppose a group of 900900 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 356356 patients who received the antidepressant drug, 113113 were not smoking one year later. Of the 544544 patients who received the placebo, 203203 were not smoking one year later. Given the null hypothesis ?0:(?1−?2)=0H0:(p1−p2)=0 and the alternative hypothesis ??:(?1−?2)≠0H, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use ?=0.01(a) The rejection region is |?|>(b) The test statistic is ?=zThe final conclustion is

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