# T test for mean annual income

Past records suggest that the mean annual income,m1 , of teachers in state of Connecticut is less than or equal to the mean annual income,m2 , of teachers in California. In a current study, a random sample of 25 teachers from Connecticut and an independent random sample of 25 teachers from California have been asked to report their mean annual income. The data obtained are as follows:

Annual income in dollars

Connecticut

61232, 52419, 41600, 60430,

60230, 51314, 64200, 48079,

52768, 46352, 48467, 47780,

46028, 54026, 55293, 51946,

46447, 47503, 51745, 47994,

51761, 47533, 37881, 47779,

56983

California

52147, 40675, 48056, 39410,

52748, 44311, 49773, 47811,

46377, 39950, 55382, 47995,

51972, 43399, 41513, 42878,

52964, 50167, 48355, 51124,

45334, 38502, 49980, 55258,

47998.

The population standard deviation for mean annual income of teachers in Connecticut and in California are estimated as 6300 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.10 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Connecticut is less than or equal to the mean annual income of teachers in California? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis Ho:

The alternate Hypothesis H1:

The Type of statistic test (Z,t,chi square,F):

The value of the test statistic (Round to at least three decimal places):

The p-value (Round to at least three decimal places):

Can we reject the claim that the mean annual income of teachers from Conneticut is less than or equal to the mean annual income of teachers from california? yes or no

#### Solution Preview

...,

52768, 46352, 48467, 47780,

46028, 54026, 55293, 51946,

46447, 47503, 51745, 47994,

51761, 47533, 37881, 47779,

56983

California

52147, 40675, 48056, 39410,

52748, 44311, 49773, 47811,

46377, 39950, 55382, 47995,

51972, 43399, 41513, 42878,

52964, 50167, 48355, 51124,

45334, 38502, 49980, 55258,

47998.

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The population standard deviation for mean annual income of teachers in Connecticut and in California are estimated as and , respectively. It is also known ...