Adam's Adv Stats & Analytics Blog

  Module 6. Assignment: Question A: A1.  Compute the mean of this population: A2.  Select a random sample of size 2 out of the five members:  I have selected (14,10) A3.  Compute the mean and standard deviation of your sample: Mean = (14+10)/2 = 12 SD = sqrt((((14-12)^2)+((10-12)^2))/(2-1)) = sqrt(8) = 2.83 A4.  Compare the Mean and Standard deviation of your sample to the entire population of this set (8,14, 16, 10, 11):   Comparison: The population mean is 11.8, whereas the sample mean is 12. Both values are close but differ due to sampling variability. The population standard deviation is about 2.86 whereas the sample standard deviation is 2.83. I believe the discrepancy is due to the sample having fewer observations and its SD using "n - 1", while population SD is only using "n".  Question B: B1. Does the sample proportion p have approximately a normal distribution? Explain : n = 100 p = 0.95 q = 1 - p = 0.05 np = 100(0.95) = 95 nq = 100(0.05...

  Module 5. Assignment: Some things to note before starting this assignment: Question A: A1:  State the null and alternative hypothesis _______ Given that: H0 = 70 σ = 3.5 n = 49 x̄ = 69.1 H0  = 70 H1 =/ 70 A2:   Is there evidence that the machine is not meeting the manufacturer's specifications for average strength? Use a 0.05 level of significance _______  I believe there isn't evidence regarding the machine not meeting the manufacturer's requirements, we have the values to compute this. To test this, we need to use the formula first: z = ( x̄-H0)/(σ/(sqrt(n)))  -> (69.1-70)/(3.5/(sqrt(49))) = -1.8 Now, we need to use this formula: Two-tailed p-value = p = 2 * pnorm(z) A3:  Compute the p value and interpret its meaning _______     As we can see, our p-value is 0.071861 = 0.072. This means that p > alpha (0.072 > 0.05). Therefore, We fail to reject the null hypothesis, meaning there isn't enough evidence that the machin...

  Module 4. Assignment: Question A:         A1: What is the probability of event A? P_Total = 10 + 20 + 20 + 40 = 90 P(A) = (10 + 20)/90 = 30/90 = 3/9 = 1/3 = 0.333333...  A2: What is the probability of event B? P(B) = (10   + 20)/90 = 30/90 = 3/9 = 1/3 = 0.333333... A3: What is the probability of event A or B? P(A   ∩     B) = 10/90 = 1/9 = 0.1111 P(A  ∪ B ) = P(A) + P(B) - P(A  ∩  B) = 1/3 + 1/3 - 1/9 = 5/9 = 0.5556 A4: What is the probability of   P(A or B) = P(A) + P(B)? P(A or B) = P(A   ∪ B) P(A   ∪ B) = P(A) + P(B) only if they're mutually exclusive. However, since they are not mutually exclusive, that means they overlap. Therefore, the probability of it happening is zero. Question B: What is the probability that it will rain on the day of Jane's wedding? P(rain) = 5/365 P(forecast rain | rain) = 0.9 P(forecast rain | no rain) = 0.1 P(rain |   forecast rain) = ((5/365)(0.9))/((5/365)(0/9)) + ((36...