An experiment is conducted to determine the effect of temperature and time on dy

Question

An experiment is conducted to determine the effect of temperature and time on dye brightness in synthetic fibers. A batch of fibers is dyed and then dried for a specific length of time at a specific temperature. Finished fibers are evaluated with a 50-point brightness index. (the higher the index, the brighter the color.) the time factor has two levels (40 minutes and 50 minutes) and the temperature factor has three levels (350 F, 375 F, and 400 F). Each cell has three replications (batches). Brightness-index data for the experiment are given below. Use these data for Questions on this task. Calculate the cell means. Calculate the test statistic F' and find the P-value for the interaction test. For alpha = 0.05, make a decision about Ho. Calculate the test statistic F' and find the P-value for the test of hypothesis of time-level means. For alpha = 0.05, make a decision about Ho.

Explanation / Answer

2)

F value for interaction = 0.1111

p-value = 0.8957

3)

We fail to reject the null hypothesis for interation this means there are not enough evidence which shows there is interaction between temperature and time.

4)

F value for time level = 9.6918

p-value = 0.0090

We reject the null hypothesis H0. This means that time-level means are not equal

Anova: Two-Factor With Replication SUMMARY A B C Total 40m Count 3 3 3 9 Sum 100 112 118 330 Average 33.3333 37.3333 39.3333 36.6667 Variance 17.3333 6.3333 12.3333 16 50m Count 3 3 3 9 Sum 121 127 134 382 Average 40.3333 42.3333 44.6667 42.4444 Variance 20.3333 12.3333 24.3333 17.7778 Total Count 6 6 6 Sum 221 239 252 Average 36.8333 39.8333 42 Variance 29.7667 14.9667 23.2 ANOVA Source of Variation SS df MS F P-value F crit Sample 150.2222 1 150.2222 9.6918 0.0090 4.7472 Columns 80.7778 2 40.3889 2.6057 0.1149 3.8853 Interaction 3.4444 2 1.7222 0.1111 0.8957 3.8853 Within 186 12 15.5 Total 420.4444 17

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