A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Arizona and Nevada. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Arizona is less than the mean annual income of childcare workers in Nevada. To see if this is true, the firm selected a random sample of 10 childcare workers from Arizona and an independent random sample of 10 childcare workers from Nevada and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Arizona 35597, 44349, 30210, 47473, 36689, 41493, 30410, 29736, 31880, 39582 Nevada 32082, 46198, 42198, 31466, 44105, 37025, 40391, 37193, 54640, 38686 Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Arizona and in Nevada are estimated as 6300 and 6500, respectively. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean annual income, u,, of childcare workers in Arizona is less than the mean annual income, l,, of childcare workers in Nevada? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)

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

(d)	Find the p-value. (Round to three or more decimal places.)

(e)	Can we support the claim that the mean annual income of childcare workers in Arizona is less than the mean annual income of childcare workers in Nevada?
Yes No

A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Arizona and Nevada. Due to recent trends in the childcare
industry, the firm suspects that the mean annual income of childcare workers in Arizona is less than the mean annual income of childcare workers in Nevada. To
see if this is true, the firm selected a random sample of 10 childcare workers from Arizona and an independent random sample of 10 childcare workers from
Nevada and asked them to report their mean annual income. The data obtained were as follows.
Annual income in dollars
Arizona 35597, 44349, 30210, 47473, 36689, 41493, 30410, 29736, 31880, 39582
Nevada 32082, 46198, 42198, 31466, 44105, 37025, 40391, 37193, 54640, 38686
Send data to calculator
Send data to Excel
The population standard deviation for the annual incomes of childcare workers in Arizona and in Nevada are estimated as 6300 and 6500, respectively. It is also
known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to support the claim that the
mean annual income, u,, of childcare workers in Arizona is less than the mean annual income, u, of childcare workers in Nevada? Perform a one-tailed test.
Then complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)

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 + ...

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