please solve these all questions:-
(In some of the exercises that follow, we must make assumptions of normal distributions with the usual notation.) In bowling, it is often possible to score well in the first game and then bowl poorly in the second game, or vice versa. The following six pairs of numbers give the scores of the first and second games bowled by the same person on six consecutive Tuesday evenings: Game 1: 170 190 200 183 187 178 Game 2: 197 178 150 176 205 153 Assume a bivariate normal distribution, and use these scores to test the hypothesis Ho: p = 0 against H, : p #0 at a = 0.10.(In some of the exercises that follow, we must make assumptions of normal distributions with the usual notation.) In a college health fitness program, let X equal the weight in kilograms of a female freshman at the beginning of the program and let Y equal her change in weight during the semester. We shall use the following data for n = 16 observations of (x, y) to test the null hypothesis Ho: p = 0 against a two-sided alternative hypothesis: (61.4, -3.2) (62.9, 1.4) (58.7, 1.3) (49.3, 0.6) (71.3, 0.2) (81.5,-2.2) (60.8, 0.9) (50.2, 0.2) (60.3, 2.0) (54.6, 0.3) (51.1, 3.7) (53.3, 0.2) (81.0, -0.5) (67.6. -0.8) (71.4. -0.1) (72.1. -0.1) (a) What is the conclusion if a = 0.10? (b) What is the conclusion if a = 0.05?Let X equal the weight in grams of a "52-gram" snack pack of candies. Assume that the distribution of X is N(0, 4). A random sample of n = 10 observations of X yielded the following data: 55.95 56.54 57.58 55.13 57.48 56.06 59.93 58.30 52.57 58.46 (a) Give a point estimate for u. (b) Find the endpoints for a 95% confidence interval for u. (c) On the basis of these very limited data, what is the probability that an individual snack pack selected at random is filled with less than 52 grams of candy?As a clue to the amount of organic waste in Lake Macatawa (see Example 7.1-4), a count was made of the number of bacteria colonies in 100 milliliters of water. The number of colonies, in hundreds, for n = 30 samples of water from the east basin yielded 93 140 8 120 3 120 33 70 91 61 7 100 19 98 110 23 14 94 57 9 66 53 28 76 58 73 49 37 92 Find an approximate 90% confidence interval for the mean number (say, =) of colonies in 100 milliliters of water in the east basin. Reference Example 7.1-4 Let X equal the weight in grams of a "52-gram" snack pack of candies. Assume that the distribution of X is /(, 4). A random sample of n = 10 observations of X yielded the following data: 55.95 56.54 57.58 55.13 57.48 56.06 59.93 58.30 52.57 58.46 (a) Give a point estimate for . (b) Find the endpoints for a 95% confidence interval for . (c) On the basis of these very limited data, what is the probability that an individual snack pack selected at random is filled with less than 52 grams of candy?tit-:zompanyr has been producing bolts that are about = 0,02 charL Then suppose that, over the next 24 hours, the following numbers of defective both; are observed: 4110521343100411620023'35 Would any action have been required during this time? Ledolter and Hogg {see References] report that, in the production 01 stainless steel pipes, the number ofdefects per 10!] feet should be controlled. From 15 randomly selected pipes of length 100 feet. the following data on the number of defects were observed: 6m3l?974513498 {a} Compute the control limits ofthe 13 chart and draw this oontrol charL [b] Is the process in statistical control
