University:
Jackson College
Course:
MAT-010 | Basic Mathematics
Academic year:

2024
Views:

344

Pages:

5
Author:

Bennett Wheeler

Question 1 9. The purpose of statistical inference is to provide information about the: a. sample based upon information contained in the population. b. population based upon information contained in the sample. c. population based upon information contained in the population. d. mean of the sample based upon the mean of the population. Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are: a. 200 and 18. b. 81 and 18. c. 9 and 2. d. 200 and 2. Answer 1 The purpose of statistical inference is to draw conclusions about the population based on sample data. So, the correct response is (b): "population based upon information contained in the sample." For question 10, using the formula for standard error of the mean 𝑆 𝐸 𝑀 = 𝜎 𝑛 SEM= n σ : 𝑆 𝐸 𝑀 = 18 81 = 2 SEM= 81 18 =2 Therefore, the mean and standard error of the mean are 200 and 2, so the answer is (d). Question 2 A statistic is an unbiased estimator of a parameter when: (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. Answer 1 The correct answer is (d): "in many samples, the values of the statistic are centered at the value of the parameter." Question 3 Find the following percentiles for the standard normal distribution. Interpolate where appropriate. a. 91st Percentage value is 91. Answer 1 The z-score corresponding to the 91st percentile is approximately 1.34. Question 4 Given 𝑋 ∼ 𝑁 ( 570 , 103 ) X∼N(570,103), find the z-score corresponding to an observation of 470. a. 0.97 b. -0.97 c. 0.64 d. -0.64 Answer 1 Using the z-score formula: 𝑧 = 𝑥 − 𝜇 𝜎 = 470 − 570 103 = − 0.97 z= σ x−μ = 103 470−570 =−0.97 So, the answer is (b): -0.97. Question 5 Which of the following are characteristics of the Normal Distribution? i. bell shaped ii. continuous iii. discrete iv. symmetric Answer 1 The correct characteristics of the normal distribution are: i. bell shaped ii. continuous iv. symmetric