# Probability And Statistics | Week 10

**Course Name: Probability And Statistics**

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**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.**

(A) (-0.25, 3.72)

(B) (-0.28,3.16)

(C) (0.28,3.21)

(D) (0.25,3.85)

**Answer: (B) (-0.28,3.16)**

**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 pdff(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

**Answer: (A) 0.1974**

**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) are7.21 8.52 6.92 11.15 14.35 7.58 6.21 9.67 10.12 12.42 13.35Find 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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**These are Probability And Statistics Week 10 Assignment 10 Answers**