Question

To compare two programs for training industrial workers to perform la skilled job, 10 workers are included in an experiment. All 10 workers were trained by both programs; 5 were trained by method 1 first and then method 2, the other 5 were trained by method 2 first and then method 1. After completion of each training, all the workers are subjected to a time-and-motion test that records the speed of performance of a skilled job. The following data are obtained.

Answer 1

If we compare the p value and the significance level assumed  we see that  so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance.

Data given and notation

We can calculate the sample mean and deviation with these formulas:

represent the mean for the sample mean for 1

represent the mean for the sample mean for 2

represent the sample standard deviation for the sample 1

represent the sample standard deviation for the sample 2

sample size selected 1

sample size selected 2

represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the average time taken when training under method 1 is less than the average time for Method 2, the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

(1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

 P-value

The first step is calculate the degrees of freedom, on this case:

Since is a one sided test the p value would be:

To learn more about  null hypothesis visit the link

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