Past records suggest that the mean annual income, μ1 , of teachers in state of pennsylvania is less than or equal to the mean annual income, μ2 , of teachers in Illinois. In a current study, a random sample of 15 teachers from pennsylvania and an independent random sample of 15 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows: Annual income in dollars pennsylvania 49204, 44644, 56205, 45100, 40385, 50560, 47642, 46225, 41540, 49653, 47472, 45562, 57841, 45448, 45279 Illinois 41795, 41712, 40832, 39785, 46177, 50496, 36066, 38146, 40326, 50170, 38444, 49513, 46034, 50010, 37844 The population standard deviation for mean annual income of teachers in pennsylvania and in Illinois are estimated as 6400 and 6100 , respectively. It is also known that both populations are approximately normally distributed. At the 0.1 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of pennsylvania is less than or equal to the mean annual income of teachers in Illinois? Perform a one-tailed test. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The critical value at the 0.1 level of significance:(Round to at least three decimal places.) Can we reject the claim that the mean annual income of teachers from pennsylvania is less than or equal to the mean annual income of teachers from Illinois? Yes No

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Past records suggest that the mean annual income,

μ1

, of teachers in state of pennsylvania is less than or equal to the mean annual income,

μ2

, of teachers in Illinois. In a current study, a random sample of

teachers from pennsylvania and an independent random sample of

teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows:

Annual income in dollars

pennsylvania

49204, 44644, 56205, 45100, 40385, 50560, 47642, 46225, 41540, 49653, 47472, 45562, 57841, 45448, 45279

Illinois

41795, 41712, 40832, 39785, 46177, 50496, 36066, 38146, 40326, 50170, 38444, 49513, 46034, 50010, 37844

The population standard deviation for mean annual income of teachers in pennsylvania and in Illinois are estimated as

6400

and

6100

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

0.1

level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of pennsylvania is less than or equal to the mean annual income of teachers in Illinois? Perform a one-tailed test.


The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF

The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.1 level of significance: (Round to at least three decimal places.)
Can we reject the claim that the mean annual income of teachers from pennsylvania is less than or equal to the mean annual income of teachers from Illinois?	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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