An investigation of the effectiveness of an antibacterial...

Name: Problem 45, Chapter 11: Basic Statistics for Business and Economics
Uploaded: 2022-04-02T16:36:27-08:00
Duration: 2 min 35 s
Channel: Sheryl Ezze
Description: An investigation of the effectiveness of an antibacterial soap in reducing operating room contamination resulted in the accompanying table. The new soap was tested in a sample of eight operating rooms in the greater Seattle area during the last year. At the .05 significance level, can we conclude the contamination measurements are lower after use of the new soap?

An investigation of the effectiveness of an antibacterial soap in reducing operating room contamination resulted in the accompanying table. The new soap was tested in a sample of eight operating rooms in the greater Seattle area during the last year. At the .05 significance level, can we conclude the contamination measurements are lower after use of the new soap?

Key Concepts

p-value

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. It provides a measure to quantify the evidence against the null hypothesis. In hypothesis testing, if the p-value is less than the predetermined significance level, the results are considered statistically significant.

Significance Level

The significance level, often denoted by alpha (?), is the threshold probability used to determine whether the observed data are sufficiently inconsistent with the null hypothesis. A common choice is 0.05, which means that if the p-value is less than 0.05, the null hypothesis is rejected in favor of the alternative hypothesis.

Paired Sample t-test

A paired sample t-test is used when comparing two related samples or measurements taken from the same subjects under two different conditions. This test accounts for the paired nature of the data, reducing variability and providing a more sensitive analysis for detecting differences due to the intervention.

Null and Alternative Hypotheses

The null hypothesis typically states that there is no difference between the measurements before and after the intervention, while the alternative hypothesis posits that the intervention has a specific effect—in this case, that the after measurements are lower. Clearly defining these hypotheses is critical for guiding the correct statistical test and interpretation of the results.

Hypothesis Testing

Hypothesis testing is a fundamental statistical method used to determine if there is enough evidence in a sample of data to infer that a certain condition holds true for the entire population. In the context of comparing pre- and post-treatment measurements, this process involves setting up a null hypothesis (no effect or no difference) and an alternative hypothesis (an effect or difference exists).

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