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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

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.

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