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Q14. In testing, H.: H=2 vs H₁: u>2 using a=0.1, a random sample of size n-6 from normal population with x=2.6, s=0.4336 is obtained. The observed test statistic ris B) 3.39 C) 1.22 A) 2.44 D) 1.13 Q15. If P(Q)-0.45, P(R)-0,3 are mutu 11

Q14. In testing, H.: H=2 vs H₁: u>2 using a=0.1, a random sample of size n-6 from normal population with x=2.6, s=0.4336 is obtained. The observed test statistic ris B) 3.39 C) 1.22 A) 2.44 D) 1.13 Q15. If P(Q)-0.45, P(R)-0,3 are mutu 11

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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pleaseee sir solve question 14 and 15

**Statistics and Probability Problems** For students learning Statistics and Probability, here are some practice problems to test your understanding: --- **Q14. Hypothesis Testing** In testing \( H_0: \mu = 2 \) vs \( H_1: \mu > 2 \) using \( \alpha = 0.1 \), a random sample of size \( n=6 \) from a normal population with \( \bar{x} = 2.6 \), \( s = 0.4336 \) is obtained. The observed test statistic \( t \) is: A) 2.44 B) 3.39 C) 1.22 D) 1.13 --- **Q15. Probabilities of Mutually Exclusive Events** If \( P(Q) = 0.45 \), \( P(R) = 0.3 \) are mutually exclusive, then \( P(Q \cap R) \) is: A) 0.3 B) 0.45 C) 0.12 D) None --- **Q16. Confidence Interval and Point Estimate** Suppose a 99% confidence interval for the population mean (\( \mu \)) is given by (123.7, 153.5). Find the point estimate of \( \mu \): A) 2.575 B) 277.2 C) 138.6 D) 137.6 --- *Assume that the random variable \( X \) is normally distributed with a mean \( \mu = 50 \) and standard deviation \( \sigma = 16 \). Answer the following two questions:* **Q17. Probability Calculation** The probability \( P(X > 70) \): A) 0.8944 B) 0.8819 C) 0.0156 D) 0 --- **Q18. Mode of a Random Variable** The mode of a random variable \( X \) is: A) 66 B) 45 C) 50 D) 3.125 --- **Q19. Standard Normal Variable** Let \( Z \) be a standard normal variable, find \( k \) such that \( P(-2 < Z < k) = 0.627 \): A) 0.3846 B) 0.3223
Transcribed Image Text:**Statistics and Probability Problems** For students learning Statistics and Probability, here are some practice problems to test your understanding: --- **Q14. Hypothesis Testing** In testing \( H_0: \mu = 2 \) vs \( H_1: \mu > 2 \) using \( \alpha = 0.1 \), a random sample of size \( n=6 \) from a normal population with \( \bar{x} = 2.6 \), \( s = 0.4336 \) is obtained. The observed test statistic \( t \) is: A) 2.44 B) 3.39 C) 1.22 D) 1.13 --- **Q15. Probabilities of Mutually Exclusive Events** If \( P(Q) = 0.45 \), \( P(R) = 0.3 \) are mutually exclusive, then \( P(Q \cap R) \) is: A) 0.3 B) 0.45 C) 0.12 D) None --- **Q16. Confidence Interval and Point Estimate** Suppose a 99% confidence interval for the population mean (\( \mu \)) is given by (123.7, 153.5). Find the point estimate of \( \mu \): A) 2.575 B) 277.2 C) 138.6 D) 137.6 --- *Assume that the random variable \( X \) is normally distributed with a mean \( \mu = 50 \) and standard deviation \( \sigma = 16 \). Answer the following two questions:* **Q17. Probability Calculation** The probability \( P(X > 70) \): A) 0.8944 B) 0.8819 C) 0.0156 D) 0 --- **Q18. Mode of a Random Variable** The mode of a random variable \( X \) is: A) 66 B) 45 C) 50 D) 3.125 --- **Q19. Standard Normal Variable** Let \( Z \) be a standard normal variable, find \( k \) such that \( P(-2 < Z < k) = 0.627 \): A) 0.3846 B) 0.3223
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