Past records suggest that the mean annual income, , of teachers in state of Texa
ID: 3311723 • Letter: P
Question
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 Virginia. In a current study, a random sample of teachers from Texas and an independent random sample of teachers from Virginia have been asked to report their mean annual income.The data obtained are as follows. Annual income in dollars Texas 39227, 27675, 30912, 27918, 28725, 45867, 29294, 24949, 35855, 35501 Virginia 37337, 40617, 35504, 37906, 33614, 39335, 30725, 39936, 37751, 40244 Send data to Excel The population standard deviation for mean annual income of teachers in Texas and in Virginia 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 Virginia? 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: H0: The alternative hypothesis: H1: The type of test statistic:The value of the test statistic: (Round to at least three decimal places.) The critical value at the level of significance: (Round to at least three decimal places.) 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 Virginia?YesNo
Explanation / Answer
From the given data we have
p-value = 0.0293
As p-value is less than the significance level 0.05, hence we reject the null hypothesis.
Yes, we can 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 Virginia
Given Data Texas Virginia Name mean 32592.3 37296.9 Sample size 10 10 Std. dev. 6432.99 3186.33