Do government employees take longer coffee breaks than private sector workers? T
ID: 3289665 • Letter: D
Question
Do government employees take longer coffee breaks than private sector workers? That is a quest that interested a management consultant. To examine the issue, he took a random sample of ten government employees and another random sample of ten private sector workers and measured the amount of time (in minutes) they spent in coffee breaks during the day. The results and analysis are shown below. Assume that the two populations are normally distributed. 6 Which is the best set of hypotheses for this experiment? H_0: x_G bar - x_P bar = 0 H_1: x_G bar- x_P bar notequalto 0 H_0: mu _G - mu _P = 0 H_1: mu _G - mu _P notequalto 0 H_0: mu _G - mu _P greaterthanorequalto 0 H_1: mu _G - mu _P 0 What is S^2_r (rounded to the thousandths place)? 13.167 18 21.228 29.289 What is the value of the test statistic? 5.7 2.766 2.1009 1.734 What implications should be drawn? There is not enough evidence to support the consultant's claim that there is a difference in the length of time government employees and private sector workers take for coffee breaks. There is enough evidence to support the consultant's claim that government employees take longer coffee breaks than private sector workers. There is enough evidence to support the consultant's claim that there is a difference in the length of time government employees and private sector workers take for coffee breaks. There is not enough evidence to support the consultant's claim that government employees take longer coffee breaks than private sector workers.Explanation / Answer
Solution:-
6) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
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).
7) sr2 = 21.228
DF = 18
t = [ (x1 - x2) - d ] / SE
8) t = 2.766
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 40 degrees of freedom is more extreme than - 2.766; that is, less than - 2.766 or greater than 2.766.
Thus, the P-value = 0.0127.
Interpret results. Since the P-value (0.0127) is less than the significance level (0.05), we cannot accept the null hypothesis.
9) (d) There is enough evidence to support the consultant's claim that there is difference in the length of time government employees and private sector workers take for coffee breaks.
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