statisitcs assignment
Stat 7 Final Exam Version B Spring 2021 Taylor Madera Center Page 1 of 4 Please show your work and submit it along with your answers as file uploads under “Assignments” in Canvas. It will be appreciated if you submit your answers in the order in which the problems appear on the exam. SECTION ONE: The Five Steps of the Hypothesis Testing Procedure Note: Please include all five steps (and number them) of the hypothesis testing procedure. Also include a diagram as illustrated in class. Five years ago, the management of the first ever Sawbucks in the lovely city of Madiera claimed that the mean number of total customers it served per day was 1,200. However, recently, a random sample consisting of 28 days revealed that a mean of 1,195 customers were being served at this particular Sawbucks daily. The known population standard deviation is 9.5 customers. At the 0.01 significance level, can we conclude that the number of customers served daily at this particular Sawbucks is less than 1,200? SECTION TWO: Areas Beneath the Normal Curve Note: For each lettered problem below, you are expected to draw a diagram similar to what was illustrated in class. The mean one-way commute to work in Rider Town is 20 minutes. The standard deviation is 3.2 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (X < 16="" mins)="" ___________________="" b).="" p="" (x=""> 15 mins) ___________________ c). P (15 < x="">< 16="" mins)="" ______________________="" d).="" p="" (15="">< x="">< 26="" mins)="" ______________________="" e).="" p="" (x=""> 26 mins) ________________________ TEST CONTINUED ON NEXT PAGE Stat 7 Final Exam Version B Spring 2021 Taylor Madera Center Page 2 of 4 SECTION THREE: Contingency Table and Probabilities The following is a contingency chart for a group of toys. Each toy is boxed in an identical container so that there is an equal chance of picking any one toy at random: (Note: Please round answer off to four digits beyond the decimal, such as 0.1234) a). A green toy or a boat? ____________________ b). A blue toy, given that the toy is a plane? __________________ c). A plane, given that the toy is brown? ________________ d). What is the probability of drawing a green boat on a first draw, and a brown plane on a second draw? ___________________ TEST CONTINUED ON NEXT PAGE Boat Plane Train Teddy Bear Totals Blue 5 10 20 25 60 Purple 20 25 25 20 90 Green 25 10 40 40 115 Brown 10 30 5 10 55 Totals 60 75 90 95 320 Stat 7 Final Exam Version B Spring 2021 Taylor Madera Center Page 3 of 4 SECTION FOUR: Completing the first two steps in the hypothesis testing procedure, plus starting the appropriate diagram as illustrated in class. Note: On these problems, you will receive no credit for work on steps 3, 4, or 5 of the hypothesis testing procedure. 1). A random sample found that 14 out of 20 Sawbucks customers rated the Rocky Marciano Special with the rating of “Excellent.” A random sample of 22 out of 30 customers at Sawbucks rated the Vince Lombardi Special as being “Excellent.” At the 0.10 significance level, can we conclude that the proportion of Sawbucks customers who rated the Rocky Marciano Special as “Excellent” differs from the proportion of customers who rated the Vince Lombardi Special as “Excellent?” 2). Historically, the mean number of passengers who fly on Delta Airlines has been 45. However, due to recent newsworthy events, some in the management at Delta feel that that number needs to be revised downward. A recent random sample of 28 Delta flights yielded a mean number of passengers of 39 with a sample standard deviation of 3.5. At the 0.01 significance level, can we conclude that the mean number of passengers on Delta flights is now less than 45? 3). The mean number of points scored per game by the Bullyard High School basketball team in a random sample of 10 games is 73, with a sample standard deviation of 2.3 points. The mean number of points scored per game by the Madiera High School basketball team in a random sample of 15 games is 68, with a sample standard deviation of 2.7 points. At the 0.05 significance level, can we conclude that the mean number of points scored by the Bullyard basketball team is greater than the mean number of points scored by those of Madiera? TEST CONTINUED ON NEXT PAGE Stat 7 Final Exam Version B Spring 2021 Taylor Madera Center Page 4 of 4 SECTION FIVE: Probability of a System Working A particular system is composed of three machines: A, B, C, and D. The entire system will work as long as any one (or more than one) of the four machines works. (With backup). P(A works) = 0.68 P(B works) = 0.75 P(C works) = 0.64 P(D works) = 0.90 Rounded to the fourth digit beyond the decimal point, P(The entire system works) = ___________________