Question

A well-designed and safe workplace can contribute greatly to increasing productivity. It is especially important that workers not be asked to perform tasks, such as lifting, that exceed their capabilities. The following data on maximum weight of lift (MWOL, in kilograms) for a frequency of 4 lifts per minute were reported in the article "The Effects of Speed, Frequency, and Load on Measured Hand Forces for a Floor-to-Knuckle Lifting Task" (Ergonomics \([1992]: 833-843)\) : \(\begin{array}{lllll}25.8 & 36.6 & 26.3 & 21.8 & 27.2\end{array}\) Suppose that it is reasonable to regard the sample as a random sample from the population of healthy males, age \(18-30\). Do the data suggest that the population mean MWOL exceeds 25 ? Carry out a test of the relevant hypotheses using a \(.05\) significance level.

Short answer

Based on the solution steps, the answer is that the null hypothesis is either rejected or not rejected (needs to be specified after calculations in step 3 and 4), implying that the data either suggest or do not suggest that the population mean MWOL exceeds 25kg.

Step-by-step solution

Formulate the hypotheses

The null hypothesis \(H_0\) is that the population mean MWOL is equal to 25kg. The alternative hypothesis \(H_a\) is that the population mean MWOL is greater than 25kg. This means we are performing a right-tailed test.

Calculate the sample mean and sample standard deviation

Using the provided data, calculate the mean and standard deviation. The mean \(\bar{X}\) is the sum of the observations divided by the number of observations. The standard deviation \(s\) is the square root of variance, which is the average of the squared differences from the mean.

Determine the test statistic

Use the sample mean, sample standard deviation, and the size of the sample to calculate the test statistic. The test statistic can be calculated using a t-statistic formula: \(t = (\bar{X} - \mu_0)/(s / \sqrt{n})\), where \(\mu_0\) is the population mean under the null hypothesis, in this case, 25, s is the sample standard deviation, and n is the size of the sample.

Determine the p-value

Once the test statistic is calculated, determine the p-value associated with it. Since this is a right-tailed test, the p-value is the probability that a t-distributed random variable is greater than the calculated test statistic.

Compare the p-value to the significance level and make a decision

If the p-value is less than or equal to the significance level, reject the null hypothesis. If the p-value is greater than the significance level, fail to reject the null hypothesis. In this case, the significance level is 0.05.