Maxforce, Inc., manufactures racquetball racquets by two different manufacturing
ID: 3044752 • Letter: M
Question
Maxforce, Inc., manufactures racquetball racquets by two different manufacturing processes (A and B). Because the management of this company is interested in estimating the difference between the average time it takes each process to produce a racquet, they select independent samples from each process. The results of the samples are shown below.
Process A
Process B
Sample Size
32
35
Sample Mean (in minutes)
43
47
Population Variance (2)
64
81
a. At the 5% level of significance do a test of whether there is a difference between the average time of the two processes. (Use Process A as Sample 1)
b. Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.
c. What if we used a 10% level of significance to test the claim? Does your conclusion change?
Process A
Process B
Sample Size
32
35
Sample Mean (in minutes)
43
47
Population Variance (2)
64
81
a. At the 5% level of significance do a test of whether there is a difference between the average time of the two processes. (Use Process A as Sample 1)
b. Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.
c. What if we used a 10% level of significance to test the claim? Does your conclusion change?
Explanation / Answer
Solution:-
a)
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).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.0771
DF = 65
t = [ (x1 - x2) - d ] / SE
t = - 1.93
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 65 degrees of freedom is more extreme than -1.93; that is, less than -1.93 or greater than 1.93.
Thus, the P-value = 0.058.
Interpret results. Since the P-value (0.058) is greater than the significance level (0.05), we have to accept the null hypothesis.
From above we do not have sufficient evidence in the favor of the claim that there is a difference between the average time of the two processes.
b) No, there is no evidence to conclude the evidence to prove that one process takes longer than the other.
c)
Thus, the P-value = 0.058.
Interpret results. Since the P-value (0.058) is less than the significance level (0.10), we have to reject the null hypothesis.
From above we have sufficient evidence in the favor of the claim that there is a difference between the average time of the two processes.