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 ?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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