The following measurements were taken on a sample n= 12 Sprucę trees selected at random from å stand. (X= diameter(cm) (at breasť height) and'Y= height (m)). The data are tabulated below: %3D 1 2 | 3 | 4 5 6 | 7 | 8 | 9 10 11 12 tree X (diam) 22.0 16.6 19.4 19.8 18.9 | 14.1 20.3 5.8 20.0 10.1 | 15.5 22.9 Y (height) | 22.3 18.8 20.2 18.0o 20.0 18.5 17.8 8.0 19.2 12.1| 16.8 19.8 Σx-2054, Σy = 211.5, Σ= 3796.38, Σ-3895.19, Σν 3817.58 1. The value of Sx is: 2. The value of Syy is: 3. The value of Sxy is: ices for 1. to 3. b) 164.7 g) 241.6 c) 167.5 h) 280.6 e) 197.4 j) 398.1 122.0 d) 177.7 i) 381.4 205.1

(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.

Let the height data (105)represent sample. Use an appropriate statistical test to check whether the population mean is different from 170 cm.Use α = 0.05.Also, write a substantive conclusion and explanation. Use an appropriate graph to check if data is normally distributed. Do it in R commander.

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