A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Indiana. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana. To see if this is true, the firm selected a random sample of 20 childcare workers from Texas and an independent random sample of 20 childcare workers from Indiana and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Texas 37093 , 33960 , 35692 , 29528 , 30978 , 35504 , 26961 , 28380 , 37537 , 25341 , 34837 , 36489 , 33633 , 41229 , 43577 , 27644 , 43364 , 28415 , 28919 , 34096 Indiana 33672 , 46452 , 35900 , 28486 , 46528 , 34252 , 40952 , 42164 , 36298 , 38828 , 32690 , 29157 , 42770 , 35527 , 40804 , 51823 , 37543 , 25530 , 37239 , 43782 Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500 , respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean annual income, μ1 , of childcare workers in Texas is less than the mean annual income, μ2 , of childcare workers in Indiana? 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.) (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 critical value at the 0.10 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana? Yes No

A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Texas and Indiana. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana. To see if this is true, the firm selected a random sample of 20 childcare workers from Texas and an independent random sample of 20 childcare workers from Indiana and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Texas 37093 , 33960 , 35692 , 29528 , 30978 , 35504 , 26961 , 28380 , 37537 , 25341 , 34837 , 36489 , 33633 , 41229 , 43577 , 27644 , 43364 , 28415 , 28919 , 34096 Indiana 33672 , 46452 , 35900 , 28486 , 46528 , 34252 , 40952 , 42164 , 36298 , 38828 , 32690 , 29157 , 42770 , 35527 , 40804 , 51823 , 37543 , 25530 , 37239 , 43782 Send data to calculator Send data to Excel The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500 , respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean annual income, μ1 , of childcare workers in Texas is less than the mean annual income, μ2 , of childcare workers in Indiana? 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.) (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 critical value at the 0.10 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana? Yes No

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Related questions

Question

childcare workers from Texas and an independent random sample of

childcare workers from Indiana and asked them to report their mean annual income. The data obtained were as follows.

	Annual income in dollars
Texas	37093 , 33960 , 35692 , 29528 , 30978 , 35504 , 26961 , 28380 , 37537 , 25341 , 34837 , 36489 , 33633 , 41229 , 43577 , 27644 , 43364 , 28415 , 28919 , 34096
Indiana	33672 , 46452 , 35900 , 28486 , 46528 , 34252 , 40952 , 42164 , 36298 , 38828 , 32690 , 29157 , 42770 , 35527 , 40804 , 51823 , 37543 , 25530 , 37239 , 43782

Send data to calculator

Send data to Excel

The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as

6200

and

6500

, respectively. It is also known that both populations are approximately normally distributed. At the

0.10

level of significance, is there sufficient evidence to support the claim that the mean annual income,

μ1

, of childcare workers in Texas is less than the mean annual income,

μ2

, of childcare workers in Indiana? 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.)

(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 critical value at the 0.10 level of significance. (Round to three or more decimal places.)

(e)	Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana?
Yes 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 + ...

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