Testing of Hypothesis

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

Annual income in dollars
Arizona 44409, 45356, 31838, 29931, 38724, 38168, 31404, 20258
Nevada 35530, 40114, 47821, 47959, 45600, 39407, 42107, 42961, 45098, 45855

The population standard deviation for mean annual income of teachers in Arizona and in Nevada are estimated as and , respectively. It is also known that both populations are approximately normally distributed. At the level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Arizona is greater than or equal to the mean annual income of teachers in Nevada? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places.

What is the null hypothesis?

What is the alternative hypothesis?

The type of test statistic? Z t F Chi Square

What is the value of the test statistic?

What is the p-value?

Can we reject the claim that the mean annual income of teachers from Arizona is greater than or equal to the mean annual income of teachers from Nevada? YES or NO

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

Annual income in dollars
Texas 22401, 30580, 37661, 33677, 41717, 25776, 37375, 39448, 31733, 32622, 25818, 34901, 38390, 47586, 33447, 35571, 39271, 38525, 36355, 31532, 46282, 40086, 29233, 35960, 43347
Indiana 44525, 37565, 44159, 38591, 47124, 39015, 49805, 42187, 43510, 41955, 31092, 42640, 33642, 48291, 42513, 45958, 41802, 35623, 35930, 30863, 52693, 41892, 28658, 43603, 35121

The population standard deviation for mean annual income of teachers in Texas and in Indiana are estimated as and , respectively. It is also known that both populations are approximately normally distributed. At the level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Texas is greater than or equal to the mean annual income of teachers in Indiana? Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places
What is the null hypothesis?
What is the alternative hypothesis?
The type of test statistic? Z t F Chi Square
What is the value of the test statistic?
What is the critical value at the 0.01 level of significance?
Can we reject the claim that the mean annual income of teachers from Texas is greater than or equal to the mean annual income of teachers from Indiana? YES or NO

Medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. The first group consisted of people with the illness, and the second group consisted of people with the illness. The first group received treatment 1 and had a mean time until remission of days, with a standard deviation of days. The second group received treatment 2 and had a mean time until remission of days, with a standard deviation of days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the level of significance, that the mean number of days before remission after treatment 1, , is greater than the mean number of days before remission after treatment 2, ?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places
What is the null hypothesis?
What is the alternative hypothesis?
The type of test statistic? Z t F Chi Square
What is the value of the test statistic?
What is the p-value?
Can we reject the claim that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after the treatment 2? YES or NO

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

Annual income in dollars
Texas 35279, 32973, 34225, 30216, 39302, 40535, 35051, 38163, 35232, 29464, 32867, 30517, 36907, 35698, 37351, 36373, 23624, 37241, 34705, 34293
Indiana 41734. 39704, 45064, 44977, 41243, 30348, 42628, 30507, 29861, 47889, 27595, 38908, 32901, 29363, 35976, 44940, 50725, 36981, 42610, 30978

The population standard deviation for mean annual income of teachers in Texas and in Indiana are estimated as and , respectively. It is also known that both populations are approximately normally distributed. At the level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Texas is greater than or equal to the mean annual income of teachers in Indiana? Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places.
What is the null hypothesis?

What is the alternative hypothesis?

The type of test statistic? Z t F Chi Square

What is the value of the test statistic?

What is the critical value at the 0.01 level of significance?

Can we reject the claim that the mean annual income of teachers from Texas is greater than or equal to the mean annual income of teachers from Indiana? YES or NO

See attached file for full problem description.