Answered: **Exercises** **7.2-1.** The length of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

7.2-2

$**Exercises** **7.2-1.** The length of life of brand $X$ light bulbs is assumed to be $N(\mu_X, 784)$. The length of life of brand $Y$ light bulbs is assumed to be $N(\mu_Y, 627)$ and independent of $X$. If a random sample of $n_X = 56$ brand $X$ light bulbs yielded a mean of $\bar{x} = 937.4$ hours and a random sample of size $n_Y = 57$ brand $Y$ light bulbs yielded a mean of $\bar{y} = 988.9$ hours, find a 90% confidence interval for $\mu_X - \mu_Y$. **7.2-2.** Let $X_1, X_2, \ldots, X_5$ be a random sample of SAT mathematics scores, assumed to be $N(\mu_X, \sigma^2)$, and let $Y_1, Y_2, \ldots, Y_8$ be an independent random sample of SAT verbal scores, assumed to be $N(\mu_Y, \sigma^2)$. If the following data are observed, find a 90% confidence interval for $\mu_X - \mu_Y$: \[ \begin{align*} x_1 &= 644, & y_1 &= 623 \\ x_2 &= 493, & y_2 &= 472 \\ x_3 &= 532, & y_3 &= 492 \\ x_4 &= 462, & y_4 &= 661 \\ x_5 &= 565, & y_5 &= 540 \\ & & y_6 &= 502 \\ & & y_7 &= 549 \\ & & y_8 &= 518 \\ \end{align*} \]$

Transcribed Image Text:**Exercises** **7.2-1.** The length of life of brand $X$ light bulbs is assumed to be $N(\mu_X, 784)$. The length of life of brand $Y$ light bulbs is assumed to be $N(\mu_Y, 627)$ and independent of $X$. If a random sample of $n_X = 56$ brand $X$ light bulbs yielded a mean of $\bar{x} = 937.4$ hours and a random sample of size $n_Y = 57$ brand $Y$ light bulbs yielded a mean of $\bar{y} = 988.9$ hours, find a 90% confidence interval for $\mu_X - \mu_Y$. **7.2-2.** Let $X_1, X_2, \ldots, X_5$ be a random sample of SAT mathematics scores, assumed to be $N(\mu_X, \sigma^2)$, and let $Y_1, Y_2, \ldots, Y_8$ be an independent random sample of SAT verbal scores, assumed to be $N(\mu_Y, \sigma^2)$. If the following data are observed, find a 90% confidence interval for $\mu_X - \mu_Y$: \[ \begin{align*} x_1 &= 644, & y_1 &= 623 \\ x_2 &= 493, & y_2 &= 472 \\ x_3 &= 532, & y_3 &= 492 \\ x_4 &= 462, & y_4 &= 661 \\ x_5 &= 565, & y_5 &= 540 \\ & & y_6 &= 502 \\ & & y_7 &= 549 \\ & & y_8 &= 518 \\ \end{align*} \]

Expert Solution

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions