2) You wish to know if the distribution of preferences for cake, ice cream, or cookies differs across men and women. The nullhypothesis is that these variables are independent; that is, the distribution is the same across men and women. You collect data from60 Americans and find the following:CakeIce Cream10-Men•Women101215Cookies85•Conduct a chi square test for independence and draw a conclusion.+3) Study and then define, give examples of, and write out notation for set, subset, union, intersection, sample space, event, andcomplement of an event.4) Consider a partition of the sample space representing possible states of reality (drug helps, null, drug hurts). You initially assumethat P(helps)=.45, P(null)=.10, P(hurts)=.45. You collect data and you find that P(data/helps)=.3, P(data null)= 2, andP(data/hurts).1. Apply Bayes Rule to compute your updated probability that the drug helps.

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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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Caden then performs a significance test. First, he performs 100 simulations. For each simulation, he randomly reorganizes the subjects into two groups, A and B, of size 10. In the simulations, group A plays the role of the treatment group and group B plays the role of the control group. After each simulation, he subtracts the average for group B from the average for group A. The distribution of the differences for all 100 simulations is shown in the histogram. 30 28 26 24 22 12 10 6. 2 Group A avg. - Group B avg. In the original experiment, the average for the treatment group was 0.8 higher than the average for the control group. Based on the 100 simulations, are the results of the experiment significant at the 5% level? yes no Number of simulations [-2.7, -2.2) [-2.2, -1.7) [-1.7, -1.2) [-1.2, -0.7) [-0.7, -0.2) [-0.2, 0.3) [0.3, 0.8) [0.8, 1.3) [1.3, 1.8) [1.8, 2.3) [2.3, 2.8)
When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a 1 1 population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is, and this is not affected by how many boys or girls have previously been born. Determine the probabilities of each sample proportion. Sample proportion of girls ▼ ▼ ▼ Probability (Type integers or simplified fractions.)
3. Can SAT scores predict college performance? Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation. A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58 The scatter diagram for the SAT score and GPA is given below: (a) Find the sample correlation coefficient r. Truncate to two decimal places. What does the value tell you about the data? (b) Find the equation of the least squares line . Truncate to four decimal places. What does the slope mean? (c) Find the value of the coefficient of determination . Truncate to two decimal places. What does this number mean? (d) What is the predicted GPA if a computer science major got a…
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An article about the California lattery gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The artide also gave Information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article. Suppose that the data resulted from a random sample of 200 lattery ticket purchasers. Based on these sample data, is it reasonable to condude that ane or more af these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with a- 0.05. (Round your answer to two decimal places.) Age of Purchaser Frequency 18-34 45 35-64 100 65 and over 55 P-value interval Op
C. Predicting Student Success STA believes there is a relationship between high school GPA (on a four-point scale) and college performance (as measured by GPA on a four-point scale). The following data were randomly selected from among students enrolling Fall 2020. HS GPA STA GPA Student 1 HS GPA STAGPA Student 21 2.9 2.5 3.6 3.4 2 3.4 3.1 3.0 22 3.4 4.0 1.7 3 3.1 23 2.9 2.9 1.7 3.0 3.2 3.3 4 24 3.5 5 3.4 25 4.0 3.6 3.6 3.0 26 3.6 3.8 3.2 3.9 3.1 27 8. 4.0 3.9 28 3.4 3.6 3.2 9. 3.0 3.0 29 3.7 10 2.9 2.0 3.0 30 4.0 3.3 4.0 3.2 11 3.3 31 12 3.6 3.8 32 3.7 3.2 3.4 3.0 13 3.7 3.9 33 14 3.8 3.6 34 2.5 2.0 15 2.5 2.5 35 2.9 2.9 3.7 2.2 16 2.9 2.5 36 3.8 17 2.8 2.1 37 2.9 18 3.8 1.7 3.5 38 3.6 3.5 3.6 19 3.7 39 3.6 20 3.9 3.0 40 3.1 3.6 How confident should St. Mary's be regarding the accuracy of their predictions? Why?
C. Predicting Student Success STA believes there is a relationship between high school GPA (on a four-point scale) and college performance (as measured by GPA on a four-point scale). The following data were randomly selected from among students enrolling Fall 2020. HS GPA STA GPA Student 1 HS GPA STAGPA Student 21 2.9 2.5 3.6 3.4 2 3.4 3.1 3.0 22 3.4 4.0 1.7 3 3.1 23 2.9 2.9 1.7 3.0 3.2 3.3 4 24 3.5 5 3.4 25 4.0 3.6 3.6 3.0 26 3.6 3.8 3.2 3.9 3.1 27 8. 4.0 3.9 28 3.4 3.6 3.2 9. 3.0 3.0 29 3.7 10 2.9 2.0 3.0 30 4.0 3.3 4.0 3.2 11 3.3 31 12 3.6 3.8 32 3.7 3.2 3.4 3.0 13 3.7 3.9 33 14 3.8 3.6 34 2.5 2.0 15 2.5 2.5 35 2.9 2.9 3.7 2.2 16 2.9 2.5 36 3.8 17 2.8 2.1 37 2.9 18 3.8 1.7 3.5 38 3.6 3.5 3.6 19 3.7 39 3.6 20 3.9 3.0 40 3.1 3.6 Is high school GPA a good predictor of STA GPA? Why? What STA GPA would you predict for a student with a high school GPA of 3.75? How you would make the prediction.
The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 96 Married, no children 29% 118 Single parent 9% 37 One person 25% 95 Other (e.g., roommates, siblings) 11% 65 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (a) What is the level of significance? State the null and alternate hypotheses. H0: The distributions are the same.H1: The distributions are the same. H0: The distributions are the same.H1: The distributions are different. H0: The distributions are different.H1: The distributions are the same. H0: The distributions are different.H1: The distributions are different. (b) Find the…
A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries. Country I Country II Country III Country IV 12.3 8.3 20.4 17.3 9.1 17.2 16.5 8.7 10.9 19.2 22.8 14.2 8.8 10.2 5.5 21.4 16.1 19.2 19.3 (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answer to three decimal places for MSBET and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Round your answer to three decimal…
3. Can SAT scores predict college performance? Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation. A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58 The scatter diagram for the SAT score and GPA is given below: (a) Find the sample correlation coefficient r. Truncate to two decimal places. What does the value tell you about the data? (b) Find the equation of the least squares line . Truncate to four decimal places. What does the slope mean? (c) Find the value of the coefficient of determination . Truncate to two decimal places. What does this number mean? (d) What is the predicted GPA if a computer science major got a…
The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Observed Number of Households in the Community Percent of U.S. Type of Household Households Married with children 26% 110 Married, no children Single parent One person Other (e.g., roommates, siblings) 29% 101 32 25% 98 11% 70 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (a) What is the level of significance? State the nul and alternate hypotheses. O Ho: The distributions are different. H: The distributions are the same. O Hg: The distributions are the same. H: The distributions are different. O Hg: The distributions are the same. H: The distributions are the same. O Hg: The distributions are different. H: The distributions are different. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test…

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