Mary Jo Fitzpatrick is the Vice President for Nursing...

Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke's Memorial Hospital. Recently she noticed that unionized jobs for nurses seem to offer higher wages. She decided to investigate and gathered the following sample information. Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the $p$ -value? Compute and interpret the $p$ -value.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. In problems involving comparing two groups, it involves setting up a null hypothesis (typically stating no difference between the groups) and an alternative hypothesis (typically stating a difference, such as one group having a higher mean than the other), then using sample data to determine whether to reject the null hypothesis.

p-value

The p-value is the probability of observing a test statistic at least as extreme as the one calculated from your sample data, under the assumption that the null hypothesis is true. It provides a measure of the strength of evidence against the null hypothesis; a small p-value indicates strong evidence in favor of the alternative hypothesis.

Significance Level

The significance level, often denoted by alpha (?), is the threshold used for determining when to reject the null hypothesis. It represents the probability of committing a Type I error, where one incorrectly rejects a true null hypothesis. In this context, if the p-value is less than the significance level (e.g., 0.02), the null hypothesis would be rejected.

Two-sample t-test

A two-sample t-test is a statistical test used to determine whether there is a significant difference between the means of two independent groups. It is particularly useful when comparing the earnings of union versus non-union nurses, as it accounts for sample variability and differences in sample sizes, and allows for the calculation of the p-value to assess the significance of the observed difference.

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