Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? Salar
ID: 3375042 • Letter: A
Question
Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? Salary show staff nurses in Tampa earn less than staff nurses in Dallas (The Tampa Tribune. January 15, 2007). Suppose that in a follow-uD study of 40 staff nurses in Tampa and 50 staff nurses in Dallas you obtain the following results. data Tampa Dallas 50 ?-559,400 s2 $7000 n, 40 = $56,100 s, = $6000 Formulate hypothesis so that. if the null hypothesis is rejected, we can conclude that salaries for staff nurses in Tampa are significantly lower than for those in Dallas. Use ? = .05. What is the value of the test statistic? What is the p-value? What is your conclusion? a. b. c. d.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1> u2
Alternative hypothesis: u1 < u2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1371.131
DF = 88
t = [ (x1 - x2) - d ] / SE
t = - 2.41
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 2.41.
Therefore, the P-value in this analysis is 0.009.
Interpret results. Since the P-value (0.009) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that salaries for staff nurses in Tampa are significantly lower than for those in Dallas.
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