Question

The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and nurses. School Teachers hers 1,095 1,076 1,077 1,125 1,034 1,059 1,052 1,070 1,079 1,080 1,092 1,082 ($) Nurses ($) 1,091 1,140 1,071 1,021 1,100 1,109 1,075 1,079 Is it reasonable to conclude that the mean weekly salary of nurses is higher? Use the 0.01 significance level. Hint: For the calculations, assume the nurses as the first sample. Click here for the Excel Data File a. Is this a one-tailed or a two-tailed test? O One-tailed test OTwo-tailed test b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject HO if t is

Answer 1

Let $\mu_1$ denotes the mean weekly salary of school teachers and $\mu_2$ denotes the mean weekly salary of nurses respectively.

To test null hypothesis HO :Mi - M2 = 0 against alternative hypothesis H1 M1-M2 < 0 Here, C1 = 1076.75, $1 = 22.8, n1 = 12, +2 = 1085.75, S2 = 34.4, n2 = 8 The test statistic can be written as: (21 – 2 – (0)) t = which under Ho follows at distribution with 11 df. where df= $6 Decision rule : We reject Ho at 0.010 level of significance if P-value < 0.010 or if tobs <-0.010,df Now, The value of the test statistic = -0.650491 associated degrees of freedom = 11 The critical value =-2.718079 P-value = P(t11 < tobs) = P(t11 < -0.650491) = 0.264364 Since p-value > 0.010 and tobs & tcritical = -2.718079, so We fail to reject Ho at 0.010 level of significance Hence, we can conclude that mean for first population is not significantly less than mean for second population.

e) ans-> Greater than 0.1.