Answered: The amount of time spent doing homework…

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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The amount of time spent doing homework for a mathematical statistics course is an important determinant of a students learning. A researcher took a random sample of the number of hours spent doing homework during a week for n =18 mathematical statistics students out of a very large population. The following are hours spent studying:

3.8, 14.1, 14.2, 4.7, 15.8, 9.6, 11.7, 12.3, 19.4, 18.7, 15.9, 12.4, 21.9, 12.6, 23.3, 13.4, 12.3, 17.0

It is reasonable to treat these measurements as coming from a normal distribution with unknown mean ? and unknown standard deviation

a)Use the data to calculate an unbiased point estimate of the true mean, ?, of weekly hours spent doing homework for mathematical statistics.

b)Use the data to find an unbiased point estimate of the population variance,

?²

of weekly hours spent doing homework for mathematical statistics.

c) Use the data to find the maximum likelihood estimate of the population variance,

?²

, of weekly hours spent doing homework for mathematical statistics.

d) Find the sample standard deviation of the above data

e) Find the sample median of the above data.

f)Create a 93% confidence interval for ?. (

)

g) What critical value did you use to calculate the 93% confidence interval in part f)?

h)Create a 93% prediction interval for ?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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