A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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- A local bank has three branch offices. The bank has a liberal sick leave policy, and the CEO was concerned with employees taking advantage of this policy. She thought that the tendency to take advantage depended on the branch at which the employee worked. To see if there were differences in the time employees took for sick leave, she asked each branch manager to sample employees randomly and record the number of days of sick leave taken during 2020. Ten employees were chosen, and the data are listed below. Do this data indicate a difference in branches? Use a level of significance of 0.05. Ho: H₂: Branch 1 Branch 2 Branch 3 Source Treatments Error Total Degrees of freedom: Rejection region: Test statistic: Decision: Conclusion: 15 11 18 df 2 7 9 20 15 19 SS 89.8333 50.6667 140.5000 19 11 23 MS 44.9167 7.2381 14 F 6.2056arrow_forwardHow young is too young to have a cell phone? A group of eighth-grade boys and girls were surveyed and asked if they had a cell phone, with the following results. Cell Phone No Cell Phone Boys 54 46 Girls 57 43 (a) Draw a stacked bar chart to describe the data. I Cell Phone I No Cell Phone 1 Cell Phone I No Cell Phone 1 Cell Phone I No Cell Phone Frequency Frequency Frequency 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20 Gender- Gender- Gender Boys Girls Вoys Girls Воys Girls Cell Phone No Cell Phone Frequency 100 80 60 40 20arrow_forwardA survey of employees at a large financial organisation was conducted to determine the overall sentiment towards various aspects of how the company operates. 30 randomly selected departments in the organisation participated in the study. Every employee in these 30 randomly selected departments filled in a questionnaire, and the data were aggregated to calculate the following two variables of interest: Rating The percentage of favourable responses (in each department) to the overall running of the company. ComplaintsThe percentage of favourable responses (in each department) to how the company handles employee complaints Source: Chatterjee, S. and Price, B. (1977) Regression Analysis by Example. New York: Wiley. (Section 3.7, p.68ff of 2nd ed. (1991).) A simple linear regression was conducted. A scatter plot of Rating versus Complaints is shown in Figure 1 and the results of the regression analysis are shown in Table 1. Rating 80 70 60 50 40 40 Model 1 Figure 1: Rating versus…arrow_forward
- A government agency computed the proportion of U.S. residents who lived in each of four geographic regions in a particular year. Then a simple random sample was drawn of 1000 people living in the United States in the current year. The following table presents the results. Region Past YearProportion ObservedCounts Northeast 0.171 150 Midwest 0.245 235 South 0.357 398 West 0.227 217 Send data to Excel Can you conclude that the proportions of people living in the various regions changed between the current year and the past year? Use the 0.05 level of significance and the P-value method with the TI-84 Plus calculator. What the P value?arrow_forwardYou may need to use the appropriate technology to answer this question. Suppose a company surveyed the work preferences and atitudes of 1,006 working adults spread over three generations: baby boomers, Generation X, and millennials. In one question, individuals were asked if they would leave their current job to make more money at another Job. The sample data are summarized in the following table. Generation Leave Job for More Money? Baby Boomer Generation X Millennial Yes 124 154 167 No 202 185 174 Conduct a test of independence to determine whether interest in leaving a current job for more money is independent of employee generation State the null and aiternative hypotheses Hg Interest in leaving job for more money is independent of the employee generation H, Interest in leaving job for more money is not independent of the employee generation. OH Interest in leaving job for mere money is mutually excusive of the employee generation H, Interest in leaving job for more money is not…arrow_forwardSecurity scans are often completed on computers in a particular college to assess the security risk from viruses etc. A sample of 120 computers which are considered at risk for viruses and other security issues are checked with a particular security scanner on a Monday and then monitored over the following week. The number of computers which broke down over the following week were recorded. The results are as follows: Security Scan (% Risk) Breakdown No Breakdown Low Risk (0 - 10%) 3 61 Slight/Moderate Risk (10 – 30%) 13 28 High Risk (>30%) 12 3 (i) Based on the above sample work out the probability that a computer in the college will breakdown. Input your answer correct to 4 decimal places here: (ii) Based on the above sample work out the probability that a computer has a low risk level OR doesn't breakdown. Input your answer correct to 4 decimal places here: (iii) Based on the above sample work out the probability that a computer has a high risk AND has a breakdown. Input your answer…arrow_forward
- The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern, measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges from 0 (less empathetic) to 28 (more empathetic). The following data, representing random samples of 8 males and 8 females, are consistent with results reported in psychological studies. Boxplots show that it is reasonable to assume that the populations are approximately normal and have equal variances. Males 13 20 14 16 13 26 21 23 Females 22 20 26 25 28 24 16 19 Can you conclude that there is a difference in mean empathy score between men and women? Use a=0.03. (1) Critical Values (Round off to 3 decimal places): (2) Test Statistic (Round off to 2 decimal places): (3) Conclusion: (Type 'Reject HO' or 'Fail to Reject HO')arrow_forwardA scientific study was conducted to determine the hours of sleep that college students get per night. The study surveyed 33 college students and obtained the following data: 7.8, 8.1, 5.9, 7.1, 6.9, 8.5, 7.8, 6.2, 6.2, 7.2, 7.1, 7.3, 6.4, 8.3, 7.9, 6.6, 7.4, 6.8, 6.7, 7.2, 5.6, 8.3, 6.6, 6, 5, 7.7, 7, 6.6, 7.8, 6.3, 7.8, 6.3, 7.1 Construct a 87% confidence interval for the average hours of sleep per night that college students get. S = τα Margine of Error: E = hours We are 87% confident that college students get an average of between hours of sleep per night. and Question Help: D Post to forum ||arrow_forwardIn the NFL, Coaches can throw "challenge" flags if they believe officials have made an incorrect call on the field. Then, based upon further analysis, the call is either overturned (because the referees were incorrect) or upheld (referees were correct). In the first eight weeks of last NFL season, there were 316 challenges made, with 154 of those calls overturned. The NFL team owners used this data to begin a lawsuit that claimed referees were wrong more than 50% of the time in challenged situations. They want to perform statistical analysis before filing that lawsuit. For the following question, select the answer which correctly responds. 0.50arrow_forward
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