Atul N Roy 5. A company has been the first choice for 70% the employment seekers in a certain region. A new management of this company has implemented new policies and think that the proportion of the \"first choice" for them has increased from 0.70. They are going to take a survey to test this statement. a) State the null and the alternative hypothesis. b) If 197 out of 269 (randomly selected sample of employment seekers) indicate this company as their first choice, write the test statistic and the P_va|ue for the hypothesis test in part a) c) Would you reject or not reject the null hypothesis at 5% level of significance. d) At 5% level of significance, Does the company have a good evidence to support that now it is the \"first choice" of more than 70% of the employment seekers? B thos.content.blackboardcdn.com G 4. A questionnaire asks the respondents to write their responses in about 100 words. To test if the mean number of words in the responses is 100 words or it is different from 100 words, a simple random sample of 12 responses will be taken. a) State the null hypothesis and the alternative hypothesis. H02y=100 HAzyathO b) The following are the word counts from a simple random sample of 12 responses. word counts 95 101 102 106 106 105 108 109 111 112 115 117 With a boxplot of this data J . , . , . 95 96 [[36 IDS 1 [0 112 Does the boxplot show any heavy outliers? Why do we have to examine this point? c) State whether you would accept or reject the null hypothesis at 1% level of significance. d) Construct a 99% condence interval for the mean of the number of words in all the responses. e) Does your 99% condence interval contain the value 100? No f) Write about relationship between a two sided hypothesis test and a related condence interval. Atul N Roy B thos.content.blackboardcdn.com G Am] N Ruy 6. To compare the cost of repairs of two different makes of cars (refer to them as \"A" and \"B" over a period of 5-years from the date of purchase, randomly selected cars of the two makes were observed and the following are the results from the samples. Repair Costs over 5- Make A Make B years Mean $2451 $2198 Standard Deviation $656 $759 Sample Size 37 40 Construct a 95% confidence interval for the difference between the mean repair costs over a period of 5-years of the cars of make A and that of make B. Write a brief statement to interpret your results. AIul N Ruy E -prodf|eet02xythos.content.blackboardcdn.Com 10f10 Assignment 4: It is a cumulative review of the Units 7-10 1. To estimate the mean time that the customers spend in a privileged lounge at an airport, the time for 35 randomly selected passengers is monitored and the mean of this sample is 97 minutes and standard deviation is 23 minutes. a) Construct a 95% confidence interval for the mean time for all the passengers. b) Construct a 99% confidence interval for the mean time for all the passengers. c) Which of these intervals is wider? . Given that the population standard deviation (7 : $275 for the expenses for the professional development activities by the employees of a LARGE company. How large a sample must be taken to construct a confidence interval for the mean expenses for the professional development activities for all the employees with a margin of error of no more than $25.00 a) with a 90% confidence b) with a 95%: confidence c) with a 99%: confidence Atul N Ray 3. A residential university system with 10005 of students takes a simple random sample of 357 students and asks them if they are satisfied with the quality of student services. If 71%: of these 357 say \"yes" a) Construct a 95% confidence interval for the mean of all the students who would say \"yes." b) What is the margin of error of the interval that you computed in the part a) c) How large a sample must be taken to construct a 95/a confidence interval for this population proportion with a margin of error of no more than i 4% points 8 -prod-f|eet02-xythos.content.blackboardcdn.com Atul N Roy 9. We are testing the hypothesis H\" : p = .75 H, : p $1200 Given that the population standard deviation is O- : $100 Find the probability of committing a type I! error if in fact ., y = $1250 Atul N Roy G -prod-f|eet02-xythos.content.b|ackboardcdn.com 7. To test of the incidence of new Vertebral fractures in 0-3 years will have a lower incidence as compared to people not receiving this treatment, the following results are obtained. Placebo Boniva Sample Size 975 977 \"In of subjects with 9.6 4.7 new Vertebral Fracture in 0- 3 yea rs Treat the above two groups as independent simple random samples. State the null and the alternative hypotheses. Find the test statistic and report your conclusion at 1% level of significance. 8 thos.content.blackboardcdn.com G Alul N Roy 10. To study if there is any relation between the gender of a student and the major that they have as their first choice in the science division, a random sample of 141 students had the following response. Female Male Mathematics 12 29 Biology 27 16 Computer Science 15 19 Chemistry 9 14 Use the Chi Square Test to determine if there is an association between the gender and the major (first choice.) Use a 5% level of significance. Atul N Roy E thos.content.blackboard dn.com G