Assignment 4A Total Marks = 75 Please show all work in the space provided. Attach additional sheets if necessary. Question 1 Grade point averages of

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Assignment 4ATotal Marks = 75Please show all work in the space provided. Attach additional sheets if necessary. Question 1Grade point averages of math majors at a large distance education university arenormally distributed with a mean of µ = 2.85 and a standard deviation of σ = 0.30.If a random sample of 25 math majors is selected from that university, what is theprobability that the sample mean grade point average will be6 marks a. either less than 2.709 or more than 2.955? 3 marks b. at least 2.757? Introduction to Statistics 27 Question 2Psychologists estimate that 80% of male drivers, when lost in trying to ﬁnd alocation, continue to drive rather than asking for directions. If this estimate iscorrect, what is the probability that, in a random sample of 100 lost male drivers,the proportion who continue to drive is4 marks3 marks 28 a. at least 0.70?b. less than 0.85? Mathematics 215 / Assignment Manual Question 3A researcher wishes to estimate the mean age of all runners who participate in theannual Vancouver marathon. A random sample of 36 participants indicated a meanage of 31.4 years. It is known that the population standard deviation of ages isσ = 7.2 years.5 marks Construct a 97% conﬁdence interval for the population mean age.Note: Express the conﬁdence interval to 2 decimal places of accuracy. Introduction to Statistics 29 Question 4A random sample of representatives from seven companies was interviewed inorder to ﬁnd the number of computers they planned to order next year. The resultsare shown below.88 marks 15 33 10 9 25 12 Assuming that the population of number of computers planned to be ordered nextyear is normally distributed, construct a 95% conﬁdence interval for the populationmean.Note: Express the conﬁdence interval to 2 decimal places of accuracy. 30 Mathematics 215 / Assignment Manual Question 54 marks Introduction to Statistics A survey is being planned to estimate, with a 98% conﬁdence interval, the meanamount of time per week that seniors spend watching television. The populationstandard deviation is known to be 5.2 hours. What sample size will be required toobtain an estimate that is within 0.5 hours of the population mean? 31 Question 6A survey was conducted to determine the percentage of students at a post-secondaryinstitution who prefer the new alpha-grading system. The responses from a randomsample of 30 students are shown below.YesNoYesYesNo7 marks NoYesNoYesYes YesYesYesNoYes YesNoNoYesNo NoYesYesNoYes YesNoYesNoYes Construct a 98.5% conﬁdence interval for the population proportion who prefer thenew alpha-grading system.Note: Express the conﬁdence interval to 4 decimal places of accuracy. 32 Mathematics 215 / Assignment Manual Question 7A researcher wishes to estimate the proportion of eligible voters who will vote for aparticular candidate in an upcoming election.4 marks a. How large should the sample size be so that a 85% conﬁdence interval for thepopulation proportion has a margin of error of 0.05? Assume that a preliminarysample suggests the proportion is 0.65. 4 marks b. Assuming that the results of a preliminary survey are not available, what is themost conservative estimate of the sample size that would limit the margin oferror to within 0.05 of the population proportion for an 95% conﬁdence interval? Introduction to Statistics 33 Question 8A study conducted last year indicated that adults spent an average of 14 hours onhousehold chores during the weekend. A research group wishes to determine if theaverage hours spent on household chores during the weekend this year is differentfrom the 14 hours of last year. Consequently, the research group selects a randomsample of 64 adults and ﬁnds the mean hours spent on household chores during theweekend to be 15.05 hours. The population standard deviation is known to be3.0 hours.8 marks 2 marks b. Would you reject the null hypothesis at α = 0.001? What would be yourconclusion? 1 mark 34 a. Formulate and test the appropriate hypotheses using the p-value approach. Whatis the p-value of the test? Would you reject the null hypothesis at α = 0.01?What would be your conclusion? c. How strong is the evidence against H0 ? [Refer to Unit 4, Section 7, in the StudyGuide.] Mathematics 215 / Assignment Manual Question 98 marks Introduction to Statistics A psychologist believes that if classical music is played during a test, test scoreswill increase. In the past, the mean test score was 60. A random sample of 49individuals wrote the test while classical music was in the background. The sampleresults showed a mean test score of 62 and a standard deviation of 6.3. Using a5% level of signiﬁcance, can the psychologist conclude that the mean test score hasincreased with classical music? Formulate and test the appropriate hypotheses. Usethe critical value approach. 35 Question 108 marks 36 A telephone company estimates that 30% of its customers are interested inhigh-speed Internet service. To test this estimate, a random sample of 100customers was selected and the results showed that 25 were interested in high-speedInternet service. Can it be concluded that the percentage of customers interested inhigh-speed Internet service is different from 30%? Formulate and test theappropriate hypotheses at a 5% signiﬁcance level. Use the critical value approach. Mathematics 215 / Assignment Manual