(a) State the null hypothesis Ho and the alternative hypothesis H. O P Ho : 1 X S p H : I (b) Determine the type of test statistic to use. (Choose one) -0 030 020 (c) Find the value of the test statistic. ( Round to three or more decimal places.) X (d) Find the critical value at the 0.10 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean annual income of childcare workers in New York isnationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York and Rhode Island. Due to recent trends in the childc dustry, the firm suspects that the that the mean annual income of childcare workers in the state of New York is greater than the mean annual income of hildcare workers in Rhode Island. To see if this is true, the firm selected a random sample of 25 childcare workers from New York and an independent randor ample of 25 childcare workers from Rhode Island and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 55597, 64294, 45588, 40421, 58575, 49083, 41474, 39910, 46817, 57960, 46384, 42002, 52075, 53829, 45684, 61231, 56655, 37986, 47912, 48870, 40385, 55439, 58262, 38696, 50401 Rhode 44278, 49851, 51616, 60502, 55496, 34803, 55116, 40525, 52440, 44201, 44043, 45671, 49991, 50375, 41602, 37073, 40405, Island 60773, 41519, 55142, 55336, 36028, 60072, 50988, 42577 Send data to calculator Send data to Excel The population standard deviations for the annual incomes of childcare workers in New York and in Rhode Island are estimated as 6400 and 6600, respectively. It is also known that both populations are approximately normally distributed. At the 0. 10 level of significance, is there sufficient evidence to support the claim that the mean annual income, , of childcare workers in New York is greater than the mean annual income, Ity, of childcare workers in Rhode Island? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)