It seems these days that college graduates who are employed full-time work more than 40 -hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 19 respondents who were college graduates employed full-time. The mean number of hours worked per week by these 19 respondents was 45 hours, with a standard deviation of 9 hours. Assume that the population of hours worked per week by college graduates employed full-time is normally distributed with mean μ . Can we conclude that μ is greater than 40 hours? Use the 0.05 level of significance. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (a) State the null hypothesis H0? and the alternative hypothesis H1? . H0:? H1:? (b) Determine the type of test statistic to use. ▼(Choose one) chi square ? z ? t ? f ? (c) Find the value of the test statistic.? (Round to three or more decimal places.) (d) Find the critical value.? (Round to three or more decimal places.) (e) Can we conclude, at the 0.05 level of significance, that the mean number of hours worked per week by college graduates is greater than 40 hours? yes or no ?

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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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It seems these days that college graduates who are employed full-time work more than 40 -hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 19 respondents who were college graduates employed full-time. The mean number of hours worked per week by these 19 respondents was 45 hours, with a standard deviation of 9 hours.

Assume that the population of hours worked per week by college graduates employed full-time is normally distributed with mean μ

. Can we conclude that μ is greater than 40 hours? Use the 0.05

level of significance.

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a)	State the null hypothesis H0? and the alternative hypothesis H1? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) chi square ? z ? t ? f ?
(c)	Find the value of the test statistic.? (Round to three or more decimal places.)

(d)	Find the critical value.? (Round to three or more decimal places.)

(e)	Can we conclude, at the 0.05 level of significance, that the mean number of hours worked per week by college graduates is greater than 40 hours? yes or no ?

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.

Expert Solution

Step 1

From the provided information,

Population mean (µ) = 40 hours

Sample size (n) = 19

Sample mean (x̅) = 45

Standard deviation (s) = 9 hours

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