Consider this scenario:  A cereal-packing company where the content of cereal boxes must have a mean of 368 grams to satisfy the labeling on the box. Because it is expensive to weigh every box produced at the factory, a sample of boxes is used to estimate the actual mean. After analyzing the data sample, the operations manager must decide whether or not the manufacturing process is working as expected. Suppose a sample of 100 boxes is taken from thousands produced during an 8-hour shift and the standard deviation (σ) of the cereal-filling process is 12, what is the standard error of the mean? Use the equation, σX̅   = σ /(square-root of n), where n is the sample size.  Enter your result as a value with one digit after the decimal point (e.g. 1.7).

(3-B is needed to answer it I am only asking for question 4.) 3) You go out and collect the following estimates of earthworms / acre:54,276 57,378 51,108 66,190 66,232 59,018 57,159These data yield the following: ̄y = 59,765.86, and s = 5,689.606a) Construct a 90% CI for these data.b) Construct a 99% CI for these data.c) Darwin once estimated that an acre of soil had about 50,000 worms in it. Is his estimateconsistent with the data above? (Historical note: His estimate was considered way too high inhis day). 4) Consider the results of 3(b). Notice that all the data fit within the 99% confidence interval. Is thisusually the case (in other words, will a 99% CI contain most of the observations)?Caution: a lot of people get this wrong! Here's a hint: suppose you had measured the worms in6000 acres (instead of just 7). What happens to the confidence interval? If you're not sure,substitute 6,000 for 7 in your calculation for (b) to see what happens.

1. Using the following data: 5568 8 9 10 10 12 15 16 19 20 20 21 24 25 25 30 32 Quartile 1 = Quartile 2 = Quartile 3 =

QUESTION 2 An environmentalist wanted to determine if the mean acidity of rain differed among Ipoh, Johor Bahru and Kuantan. He randomly selected six rain dates at each city and obtained the following data: Table 2 Ipoh 5.10 5.00 4.91 5.12 4.78 5.20 Johor Bahru 4.80 4.15 4.42 4.65 4.87 4.10 Kuantan 5.45 6.23 5.55 5.10 5.42 5.25 Answer the following questions without using any output from any software. a) Construct a complete Analysis of Variance table. b) At <= 0.05, test whether the mean acidity of rain is different among the three cities. c) Based on the answer in (a) and (b), write a brief conclusion on the mean acidity of rain among Ipoh, Johor Bahru and Kuantan.