You have been asked to determine if two different production processes have diff
ID: 3367277 • Letter: Y
Question
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process l has a mean defined as ?? and process 2 has a mean defined as u2. The null and alternative hypotheses are as follows: The populations variances are known: the known variance for process 1 equal to 1600 and the known variance for process 2 equal to 900. The sample mean of a random sample of 36 observations from process 1 is 50 and the sample mean of 25 observations from process 2 is 65 Test the null hypothesis at the 5% level. (2)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. 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 of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 8.9691
DF = 59
t = [ (x1 - x2) - d ] / SE
t = - 1.67
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 - 1.672.
Therefore, the P-value in this analysis is 0.941
Interpret results. Since the P-value (0.941) is greater than the significance level (0.05), we cannot reject the null hypothesis.
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