Lester Hollar is vice president for human resources for a...

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the $p$ -value. $$ \begin{array}{|lcc|} \hline \text { Employee } & \text { Before } & \text { After } \\ \hline \text { Bauman } & 6 & 5 \\ \text { Briggs } & 6 & 2 \\ \text { Dottellis } & 7 & 1 \\ \text { Lee } & 7 & 3 \\ \text { Perralt } & 4 & 3 \\ \text { Rielly } & 3 & 6 \\ \text { Steinmetz } & 5 & 3 \\ \text { Stoltz } & 6 & 7 \\ \hline \end{array} $$

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the $p$ -value.
$$
\begin{array}{|lcc|}
\hline \text { Employee } & \text { Before } & \text { After } \\
\hline \text { Bauman } & 6 & 5 \\
\text { Briggs } & 6 & 2 \\
\text { Dottellis } & 7 & 1 \\
\text { Lee } & 7 & 3 \\
\text { Perralt } & 4 & 3 \\
\text { Rielly } & 3 & 6 \\
\text { Steinmetz } & 5 & 3 \\
\text { Stoltz } & 6 & 7 \\
\hline
\end{array}
$$

Key Concepts

Null and Alternative Hypotheses

The null hypothesis typically claims that there is no effect or no difference—in this context, that the intervention has not reduced absenteeism. The alternative hypothesis suggests that there is a significant effect—in this case, that absenteeism has declined after the intervention. Clearly defining these hypotheses is crucial for guiding the statistical testing process.

p-Value and Statistical Significance

The p-value is the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. It provides a measure of the strength of evidence against the null hypothesis. A p-value lower than a predetermined significance level (commonly 0.05) indicates that the observed effect is statistically significant, leading to the rejection of the null hypothesis.

Paired Sample Design

A paired sample design involves collecting observations from the same subjects under two different conditions or at two different time points. This design is used to control for individual variability, since each subject acts as their own control, and it is particularly useful when testing the effect of an intervention or change over time.

Paired Sample t-Test

The paired sample t-test is a statistical technique used to compare the means of two related groups. It assesses whether the average difference between paired observations is statistically significantly different from zero, under the assumption that the differences are normally distributed. This test is appropriate when the data are collected in pairs and are not independent.

Hypothesis Testing

Hypothesis testing is a fundamental procedure in statistics that involves formulating a null hypothesis and an alternative hypothesis, and then using sample data to determine whether there is sufficient evidence to reject the null hypothesis. This process helps in making inferences about a population based on sample data.

Transcript

Please give Ace some feedback