Statistic questions. Please solve it in detail step by step.

QQuestion : The following data represent the running times of films produced by two motion picture companies : company Time ( minutes ) 102 86 198 109 92 2 81 165 97 34 92 87/114 Assuming that the populations of concern are normally distributed; a) Test the hypothesis that the average running time of films produced by company 2 exceeds the average running time of films produced by company 1 by 10 minutes against the alternative that the difference is less that 10 minutes . Use a O.I level of signifance. 6) Explain why the test you applied in port(al appropriate. C ) What is the size of the test you applied in part (a). d) Display the critical region on the corresponding distribution graph. el Using a signifinance level of 0.05, check the equality of the variances though constructing an appropriate confidence interval and comment on it. Question 2: A study on the efficiency of two different methods, isotopic method and test weighing method, to measure the amount of breast milk ingested by infants was conducted by Department of Nutrition and Dietetics at Istanbul Kultur University. In this study, intake amount using the measurement methods are listed for ten randomly selected infants as follows: infant 2 13 4 5 6 7 8 g to Isotopic Method 1663 1764 1347 1550 1465 1278 20+1 1009 1785 1410 Test - weighing 1518 1224 1562 1732 1722 1468 1715 1107 1952 1435 Method Difference 145 540 - 215 - 182 -257 -190 2% -98 167 325 Assuming that the population distribution of differences is normal; a) Does it appear that the true average difference between intake values measured by the two methods is something other than zero? ( Take the signifance level xx= 0.05) b) Construct a two-sided 95% confidence interval on the true average difference between intake values measured by the two methods. Question 3: Suppose you collect data on the number of accidents in 48 months at Space Center Houston, which are given as follows: Month 2 3 4 5 6 7 8 9 10 11 12 Using of = 0.05 Number of Accidents O 2 0 4 0 2 3 0 2 3 signifance level. Month 13 14 15 16 17 18 19 20 21 22 / 23 24 Number of Accidents O 2 3 4 2 2 2 Month 25 26 28 291 30 31 132 33 34 35 36 Number of Accidents/ O 2 2 2 2 2. Month 37 38 39/ 40 41 42 43 44 45 46 / 47 48 Number of Accidents | 2 2 2 3 3 2 2 5 0 1 a) Test if there accidents follow a Poisson distribution with a mean rate of 2 accidents per month b) What is the degrees of freedom that you use for finding the critical value in part a? why did you choose that value ? Explain