These are Probability And Statistics Week 10 Assignment 10 Answers
Q1. Nine wafers are baked at two different temperatures, 90°C and 100°C, to examine the impact of temperature on the weights (in gm) of wafers of a specified size. Find a 95% confidence interval on the difference in means assuming that the measurements in the two columns follow independent normal distributions with distinct variances.
Q2. Suppose X₁, X₂,…., Xm are m independent and identically distributed random samples from a uniform [0, θ] distribution. Which of the following is/are unbiased estimator(s) of θ? (A) 2X (B) m+1/m X(m) (C) X (D) m/m -1 X(m) Here X = 1/mΣm i=1 Xi and X(m) = max Xi.
Answer: A, B
These are Probability And Statistics Week 10 Assignment 10 Answers
Q3. Let X₁,…, Xn be independent and identical random samples from a gamma distribution with pdf f(x; a) = 1/acr(c) -xc-¹e-(a), x ≥ 0, where c> 0 is known. Which of the following is UMVUE of a? (A) X (B) X/c (C) Σn i=1 Xi (D) 1/cΣn i=1 Xi
Answer: (B) X/c
Q4. A group of 10 patients has mean weight 230 pounds. The sample standard deviation is given as 20 pounds. What is the 95% confidence interval for a sample for the true mean weight? (A) (218.407,241.593) (B) (217.604,242.396) (C) (215.694,244.306) (D) (219.565,240.436)
Answer: (C) (215.694,244.306)
These are Probability And Statistics Week 10 Assignment 10 Answers
Q5. For a normal population with known standard deviation o, what is the confidence level for the interval (A) 0.1974 (B) 0.5987 (C) 0.6046 (D) 0.4013
Q6. Independent random samples of sizes n₁ and n₂ are taken from two normal populations with variances of σ²1 and σ²2 respectively. Let n₁ = 15 and n₂ = 10 and the sample variances from the two samples be 25.7 and 29.2 respectively. Find a 90% confidence interval of σ²2/σ²2. (A) (0.4294,3.4375). (B) (0.4924,3.4735). (C) (0.3294,2.3375). (D) (0.2154,4.9275).
Answer: (A) (0.4294,3.4375).
These are Probability And Statistics Week 10 Assignment 10 Answers
Q7. Let X₁,…, Xm be a random sample from Bernoulli distribution with parameters p, 0 < p < 1. Which of the following is an unbiased estimator of p(1-p)? (A) m/m-1 X(1 + X) (B) m/m-1 X(1 – X) (C) m/m+1 X(1 + X) (D) m/m+1 X(1 – X)
Answer: (B) m/m-1 X(1 – X)
Q8. Consider eight pairs of zinc concentration of in bottom water and surface water are as follows
Construct 95% confidence interval for mean difference between bottom and surface water. (A) (0.075,0.222) (B) (0.055,0.239) (C) (0.315,0.689) (D) (0.072,0.568)
Answer: (B) (0.055,0.239)
These are Probability And Statistics Week 10 Assignment 10 Answers
Q9.
Answer: (B)
Q10. A farmer weighs 11 randomly chosen pumpkins from his farm and obtained the weights (in lbs) are 7.21 8.52 6.92 11.15 14.35 7.58 6.21 9.67 10.12 12.42 13.35 Find 95% confidence interval for population variance (σ²) assuming the the weight is normally distributed with unknown mean μ and unknown variance σ². (A) (5.84,21.92) (B) (3.74,23.59) (C) (4.82,21.64) (D) (2.31,17.56)
Answer: (B) (3.74,23.59)
These are Probability And Statistics Week 10 Assignment 10 Answers
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