436 stats final scores a it is left skewed because

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4.36 Stats final scores (a) It is left skewed because the skewness is in the direction of the mean (b) Since the median is 74 and mean is 70, so most students scored above 70 points (c) No. because the distribution is skewed not normal (d) Standard error = SD / SQRT (40) = 1.58 P (x>75) = P (Z> (75-70)/1.58)) = 1- P (Z<3.165) = 1 0.9992 = 0.0008 (e) When sample size = 20 Standard error = 10 / SQRT (20) = 2.236 So the standard error will change from 1.58 to 2.236 4.40 CFLBs (a) (10500 9000) / 1000 = 1.5 P (Z > 1.5) = 1 0.9332 = 0.0668 (b) Mean = 9000 Standard deviation of sample mean = 1000 / SQRT (15) = 258.198 (c) (10500 9000) / 258.198 = 5.81 P (Z > 5.81) = 1 P (Z < 5.81) = 1 1 = 0
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(d) (e) No. we cannot estimate them without normality. 4.44 Nearsighted (a) H o: P = 0.08 H a: P ≠ Ϭ.Ϭ8 (b) P = 21/194 = 0.108 (c) Z = (0.108 0.08) / 0.0195 = 1.44 (d) P value = 2* (1 P (Z < 1.44)) = 2 * 0.0749 = 0.1498 (e) Because P value is greater than 0.05, so null hypothesis is not rejected at 5% level of significance. These data does not provide evidence that the 8% value is inaccurate. 4.48 Same observation, different sample size The formula to calculate Z need sample size. So when n increase the test statistic will also increase. So when the test statistic s value increases, the P value decreases.
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