TemperatureLab 11 – Exam ReviewQuestion 1) As a plant manager we know from experience that the time to assemble a component T~ N(15, 4). You measure 16 people from day shift (X) and 9 people from the night shift (Y).1a) Assuming day and night shift have the same distribution, what is the mean and standard deviation of 1b) You noticed that 16 people on the day shift and 9 people on the night shift averages that differed by 1.5 seconds. Is this difference just random variation or is this difference big enough to be confident that the night shift is goofing off?16 day shift 9 night shift find Question 2) A cable car has a load capacity of 5000 lb. Assume that the weight of a randomly selected person is given by a normally distributed random variable W with mean 175 lb and a standard deviation of 20 lb. Determine the maximum number of passengers allowed on the cable car so that their weight exceeds the 5000-lb weight limit with probability less than 0.05.Xi ~ N(175, 20) find n such that P(xbar > 5000/n)  0.05Question 3) In general we want to know the percentage of Grinnell College Students who would like to start classes earlier Fall semester in order to have a full week off for Thanksgiving break. You sample 500 students, 275 say yes. Construct a 99% CI. Does it include .5?Question 4) We randomly sampled 15 bags of M&Ms to determine the number in each bag.83 75 62 89 81 92 76 78 91 76 84 79 72 79 854a) Find the mean and standard deviation.4b) Do a 95% hypothesis test to prove the average number of M&Ms is not equal to 75.4c) Construct a 95% CI. Does it include 75?4d) Do a 99% hypothesis test to prove the average number of M&Ms is not equal to 75.4e) Construct a 99% CI. Does it include 75?Question 5) An opinion poll asks a SRS of 1500 adults "Do you happen to jog?". Suppose that p = .15.What is the mean and standard deviation of p.What do we need to know before we use the normal distribution to approximate the distribution of p .Find P( p > .16)Question 6) In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius:Temperature 545o550o555oProbability .26 .32What is the probability of having a temperature of 555o?What is the probability that the temperature is greater than 545o?Find the mean and standard deviation of a random temperature sample (X).Find the mean and standard deviation of Y = 1.8X + 32. In other words convert the mean and std dev to Fahrenheit.5.14x16y)5.1(  xyPXY Question 7) In each of the following cases, state whether or not the normal approximation to the binomial should be used for a significance test on the population proportion p a) n=100 and Ho: p=.6 b) n=10 and Ho: p=.4 c) n=10000 and Ho: p=.997 d) n=150 and Ho: p=.975Question 8) Is there a relationship between smoking and emphysema? Patients were classified according to 2 criteria, the number of packs of cigarettes smoked per day and the severity of emphysema.B1-mildestform ofemphysemaB2 B3 B4-most severtype ofemphysemaLess than 1 pack a day 41 28 25 61-2 packs a day 24 116 46 14More than 2 packs a day 4 50 34 12400What is your null and alternative hypothesis?What is the value of your test statistic?What is the chi-square table value?Do you fail to reject or reject Ho?Give a range for the P-value.Explain why (or why not) you believe the amount you smoke has an impact on the severity of emphysema. Question 9) Majors for men and women in business. We sent questionnaires to 722 members of the senior class in the college of Business Administration at the University of Illinois. One question asked which major within the business program the student had chosen. Obs Accounting Administration Economics Finance ExpFemale 69 91 5 61Male 56 40 6 5910_a) 2 of the observed cell counts are small, are the expected cell counts large enough to use the chi-square approximation? 10_b) Is there a statistically significant relationship between gender and major of business students?State the null and alternative Hypothesis.Give the test statistic X2Give the p-valueDo you reject or fail to reject Ho? Does gender significantly impact the major of business students?10_c) What % of the students did not respond to the questionnaire? Does this weaken our