6. The amount of time lost during the month due to accidents was determined befo
ID: 3316007 • Letter: 6
Question
6. The amount of time lost during the month due to accidents was determined before and after a new safety program was instituted at a manufacturing firm. The sample sizes (number of months), means, and standard deviations are shown below. Sample Size Sample Mean Sample Standard BEFOREAFTER 25 97.3 12.0 16 80.1 14.0 deviation Do these data indicate that the safety program was effective in reducing the true average time lost due to accidents? Write your conclusion based on an appropriate test of hypothesis at 5% level. a. b. Write the necessary assumptions needed for your answers in (a) to be valid.Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Before< After
Alternative hypothesis: Before > After
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means 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 offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 4.244
DF = 39
t = [ (x1 - x2) - d ] / SE
t = 4.05
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 4.052. We use the t Distribution Calculator to find P(t > 4.05)
Therefore, the P-value in this analysis is less than 0.0001.
Interpret results. Since the P-value (less than 0.0001) is less than the significance level (0.05), we have to reject the null hypothesis.
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