Question

The manager of a door-making company would like to estimate the amount of time it takes for a piece of wood to be moved, cut, and packaged at two different plants. At Plant A, the manager observed 21 pieces that processed with an average time of 14.2 minutes and standard deviation of 2.6 minutes. At the second plant, the manager observed 19 pieces with an average time of 13.1 minutes with a standard deviation of 1.9 minutes.

a. Test whether there is a difference between mean process times of Plants A and B with an assumed α = 0.1. State your conclusion properly with context.

b. What three assumptions are required to perform the above test?

c. Using the above information and α = 0.1 significance level, test to see if the plants have different variability. State your conclusion properly with context.

Answer 1

A)H₀: (vs) H_a :

Test statistic is

t= 1.514

Critical value is t_0.1,38 = 1.30

Since t_cal>t_.1,38 , we reject H₀ and conclude the difference in mean of two processes is significant

B)The assumptions of the two-sample t-test are:
1. The data are continuous (not discrete).
2. The data follow the normal probability distribution.
3. The variances of the two populations are equal. (If not, the Aspin-Welch Unequal-Variance test is used.)
4. The two samples are independent. There is no relationship between the individuals in one sample as
compared to the other (as there is in the paired t-test).
5. Both samples are simple random samples from their respective populations. Each individual in the
population has an equal probability of being selected in the sample.

C) Hypothesis

(vs)

Test statistic is

F=1.873

Critical value is F_20,18,.1 = 1.84

Since F_cal>F_20,18,.1,we reject H₀ and conclude there is significant difference in variation of two processes