7. A study reported that 49 % of eighth-graders in the U.S. believe that smoking one pack of cigarettes a day does notpose a serious risk to their health. A researcher wanted to check whet her this result still holds true for the currentpopulation of eighth graders in the U.S. A random sample survey of 400 eighth-graders from the U.S. recently showedthat 176 of them believe that smoking one pack of cigarettes a day does not pose a serious risk to their health.Using 5 % significance level Test if the current proportion of all U.S. eight h-graders who hold this opinion is significantlyless than the 49%. ( State a null hypothesis H, and an alternative hypothesis Hạ, then perform the test ).8. The continuous random variable X measures the concentration of ethanol in a chemical solution and the continuousrandom variable Y measures the acidity of the solution. Suppose the variables have the following joint probabilitydensity function (pdf):f (r, y) = {-{s20 – z – 2y) if 0Sa5 5, 0Sy 55elsewhere(a) Find the marginal probability density function f, (y).(b) Find the probability P(Y >1+x).(c) Find the expectation of the product of ethanol concentration and acidity, denoted E (XY).

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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8. Has the percentage of registered nurses earning more advanced academic degrees changed? In 1980 55% of registered nurses had a high school diploma as their highest level of education, 18% had an associate's degree, 22% had a bachelor's degree, and 5% had a master's degree. In 2012, a random sample of 800 registered nurses was obtained. Of those sampled, 111 had a high school diploma as their highest educational degree, 295 had an associate's degree, 289 had a bachelor's degree, and 105 had a master's degree. At the 5% significance level, what conclusion can be reached? slom Sor pot combcee
An article published in the “American Journal of Public Health” describes the results of a health survey administered to 119 male convicts, 50 years of age or older, residing in a state social rehabilitation center. It was found that 21.6% of them claimed to have a history of venereal diseases. Based on these findings, we wish to evaluate whether more than 15% of this population has a history of venereal diseases. After evaluating the information, what would be the conclusion? A. In the population of male convicts aged 50 years or older, residing in the state social rehabilitation center, more than 15% have a history of venereal diseases. B. In the population of male convicts aged 50 years or older, residing in the state social rehabilitation center, it is not possible to say that more than 15% have a history of venereal diseases. C. In the population of male convicts aged 50 years or older, residing in the state social rehabilitation center, on average more or less 21.6% have a…
According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 0.37. Jason conducts a survey of thirty 20- to 24-year-olds who live on their own and finds that 16 do not have a landline to their home. Does this provide sufficient evidence to conclude that the proportion of 20- to 24-year-olds who live on their own and don’t have a landline is greater than 0.37? Use an a=0.10 level of significance. Note
1. In 1955, Life Magazine reported that a 25-year-old mother of 3 children, worked an average of 80 hours each week. Recently, some researchers have been studying whether the women’s movement has resulted in an increase in the work week hours for women (combining employment and at-home work). A study was done to find out if the mean work week has, in fact, increased. A random sample of 81 women were surveyed and the mean was 83 hours with a standard deviation of 10. Using a 95% confidence level, does the sample data support the researcher’s claim that the average number of weekly hours that women work, is greater than 80? a. What statistical test will you use to test this data ? b. State the null and alternative hypothesis. i. H0: ii. Ha: c. What are the confidence intervals? d. What is the value of the test statistic? e. What is the p-value? f. Circle/highlight the correct decision about the null hypothesis. Reject H0…
Labor Day was created by the U.S. labor movement over 100 years ago. It was subsequently adopted by most states as an official holiday. In a poll by Gallup, 1000 randomly selected adults were asked whether they approve of labor unions; 650 said yes. In 1936, about 72% of Americans approved of labor unions. At a 5% level of significance, do the data provide sufficient evidence to conclude that the percentage of Americans who approve of labor unions now has decreased since 1936? Solve using the critical-value approach. Define the parameter we are testing and setup a hypothesis test to see if less than 72% of Americans approve of labor unions currently. Calculate the test statistics for this hypothesis test. What is the critical value for this hypothesis test?
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One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, μ , among the general population on this subsection. The website reports that μ is 148 , but you believe that μ is greater than 148 . You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 152 and that the standard deviation of their scores is 28 . Based on this information, answer the questions below. What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 : μ is H1 : μ is In the context of this test, what is a Type I error?A Type I error is the hypothesis that μ is when, in fact, μ is .Suppose that you decide not to…
Anterior cruciate ligament (ACL) injuries occur most frequently in planting and cutting sports such as basketball, soccer, and volleyball. National collegiate athletic association injury data show that female athletes injure the ACL more frequently than their male counterparts do. A sports medicine professor wants to test this claim. He surveyed 5 universities that had both men's and woman's basketball, soccer, and volleyball and asked them how many grade 3 ACL tears they had during the past 5 seasons. Using the following results, are women at greater risk than men for ACL injuries? (use a standard deviation of 0.01, one tail test). Women- 4,3, 5, 2,4 Men- 2, 0, 1 ,2, 1 What is the difference between a repeated measure study and a matched pairs study?

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