# Past records suggest that the mean annual income,M1, of teachers in state of pennsylvania is less th

Past records suggest that the mean annual income,M1, of teachers in state of pennsylvania is less than or equal to the mean annual income,M2, of teachers in Illinois. In a current study, a random sample of 10 teachers from pennsylvania and an independent random sample of 10 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows:

Penn: 37690, 46247, 48701, 34034, 57917, 48242, 50458, 51369, 38914, 47479

Illi: 37791, 39098, 50192, 48432, 38754, 43492, 38217, 53576, 51972, 55200

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 level 0.01 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. Then fill in the table below.

Null hypothesis:

Alternative Hypothesis:

The type of test statistic (plus degrees of freedom if t)

Value of test statistic:

The critical value at the 0.01 level of significance rounded to at least 3 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?