Question

A company is manufacturing cotton threads under different speeds of spindle. The
tensile strength of the thread is a parameter that is of interest to the customer. Data
on different speeds of spindle and corresponding tensile strength on 5 samples is
given. Perform ANOVA to find out which is the most suitable speed for the
spindle so as to have maximum tensile strength.

Speed Tensile strength
1 2 3 4 5
10 22.2 20.6 21.5 20.6 22.0
20 24.2 25.0 24.8 20.7 21.0
30 25.0 23.2 21.7 22.5 20.9

Answer 1

Answer on Question #55139 – Math – Statistics and Probability

A company is manufacturing cotton threads under different speeds of spindle. The tensile strength of the thread is a parameter that is of interest to the customer. Data on different speeds of spindle and corresponding tensile strength on 5 samples is given. Perform ANOVA to find out which is the most suitable speed for the spindle so as to have maximum tensile strength.

Speed Tensile strength

Solution

The null hypothesis: the mean (average value of the dependent variable) is the same for all groups (it means that tensile strength doesn't depend on the speed for the spindle).

The alternative hypothesis: the average is not the same for all groups (it means that tensile strength depends on the speed for the spindle).

The problem can be solved using Anova: Single Factor from Analysis Tools in Microsoft Excel 2013.

The p-value for the F (1.657) is 0.2315 in our case. Let $\alpha = 0.05$. Because $P > \alpha$, we fail to reject the null hypothesis, and we conclude that there is no sufficient evidence to indicate that at least one group has a different average tensile strength.

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