(i) A(i) B(i) C(i) D(i) E(i) F(i) G(i) H(i) 1 30.71 7.16 37.79 30.41 91.64 8.67

Question

(i) A(i) B(i) C(i) D(i) E(i) F(i) G(i) H(i) 1 30.71 7.16 37.79 30.41 91.64 8.67 60.90 28.12 2 47.92 46.19 59.69 25.93 56.74 38.52 20.00 25.38 3 15.29 31.81 57.60 25.59 9.74 26.23 39.24 14.70 4 21.10 36.98 37.07 36.54 12.10 8.05 16.04 26.68 5 21.37 56.13 44.43 38.03 15.13 14.36 24.68 21.52 6 38.06 7.59 32.16 21.15 114.30 50.54 58.33 26.56 7 20.50 6.69 31.79 38.42 28.70 20.52 18.27 29.75 8 20.32 17.87 51.93 19.64 32.80 2.91 20.53 22.85 9 41.56 54.18 52.37 39.74 10.71 16.79 60.57 22.51 10 37.73 22.24 17.84 20.29 21.61 80.44 22.34 31.35 11 35.74 35.72 31.37 27.01 46.82 38.41 33.88 36.27 12 32.50 36.70 43.13 32.50 80.45 5.41 30.55 39.68 13 11.98 51.53 33.61 33.69 3.75 12.50 4.15 23.56 14 35.82 26.79 33.99 35.92 1.42 13.74 21.15 26.23 15 8.20 41.39 35.52 29.21 15.63 6.56 52.96 22.39 16 42.63 4.04 30.28 34.98 1.66 3.04 52.85 31.58 17 43.58 39.20 25.38 41.41 32.65 9.70 19.44 32.56 18 25.48 21.09 32.56 20.52 24.83 59.70 29.10 38.12 19 23.02 28.22 10.63 34.28 22.49 75.45 57.89 38.71 20 47.23 62.78 63.05 13.62 11.49 12.17 6.56 22.23 21 39.29 7.47 50.07 36.57 26.67 2.44 10.74 57.02 22 27.76 38.21 15.10 38.91 3.75 42.33 41.54 33.92 23 39.52 20.66 44.80 25.54 25.06 2.88 12.92 23.74 24 37.25 6.18 38.96 32.13 0.26 30.42 43.40 37.10 25 35.00 23.30 26.93 38.03 119.75 14.64 46.52 25.62 26 55.01 31.61 11.09 26.69 2.95 43.65 26.35 35.04 27 19.77 37.97 38.61 30.64 18.75 26.32 18.00 28.79 28 22.21 5.46 36.08 25.53 12.96 51.04 26.07 16.52 29 44.70 16.11 30.18 15.74 63.50 15.18 35.65 23.92 30 44.39 44.85 15.42 29.19 48.57 3.80 13.74 37.99 31 29.91 36.87 21.15 38.42 34.72 5.43 31.63 26.80 32 49.33 23.84 24.65 28.47 0.55 3.78 24.03 26.92 33 37.82 9.49 20.67 23.06 5.07 19.08 15.83 39.96 34 21.33 14.14 48.74 18.73 55.49 13.61 20.28 20.69 35 27.81 32.09 15.74 28.27 40.30 34.18 51.98 60.60 36 36.41 68.44 33.36 21.97 9.80 15.33 42.06 29.02 PART 1-Data Sheet #1 (Excel Spreadsheet #1) contains sample values for a set of 8 datasets. Question 1: It is claimed that each of the datasets come from populations that have = 30 and variance 2-144. For each dataset, we consider the null hypothesis 30 (and Ho: Population from which this sample was drawn has mean variance 2 = 144 ). Since the underlying distribution is unknown, we do not know the exact distribution of the sample mean. However, we can use the Central Limit Theorem to estimate the variance (and standard deviation) of the sample mean based on the claimed variance and known sample size. a) Evaluate a 95% probability range of values for the sample mean assuming Ho is true (i.e. a value for the mean of a random sample will be outside this range with probability 0.05 or less, ie. = 0.05). b) Compute the sample mean for each of the 8 datasets c) Use the results of part b) and a) to determine whether Ho should be accepted or rejected for each of the datasets.

Explanation / Answer

(a) Here population mean = 30

and varaince 2= 144

Here sample size of each population is = n = 36

standard error of sample mean se0= sqrt(2/n) = sqrt (144/36) =2

so 95% confidence interval = +- Z95% se0 = 30 +- 1.96 * 2 = (26.08, 33.92)

(2) Now we will caluclate sample mean of each dataset

(iii) Here The results are

So except Data set C and Dataset F, for all data set null hypothesis could be accepted. For other dataset C and F, we shall reject the null hypothesis.

(i) A(i) B(i) C(i) D(i) E(i) F(i) G(i) H(i) Average 32.45139 29.19417 34.27056 29.35472 30.63361 22.995 30.83806 30.12222

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