Question

A sample of 516 school teachers, who are married, showed that 205 of them hold a second job to supplement their incomes. Another sample of 383 school teachers, who are single, showed that 130 of them hold a second job to supplement their incomes. The null hypothesis is that the proportions of married and single school teachers who hold a second job to supplement their incomes are not different. The alternative hypothesis is that the proportions of married and single school teachers who hold a second job to supplement their incomes are different. The significance level is 5%. Use the normal distribution calculator to calculate the p-value. z=:P(Z≤z)= What is the p-value for this test, rounded to three decimal places?

Answer 1

The p-value for the test comparing the proportions of married and single school teachers holding a second job is determined using the 2-PropZTest function, compared against a 5% significance level to make a decision about the null hypothesis.

Step-by-step explanation:

To calculate the p-value for the hypothesis test comparing the proportions of married and single school teachers who hold a second job, we must use the 2-PropZTest function on a statistics calculator. We will first calculate the test statistic (z-value) and then the p-value.

The steps to follow would typically include finding the proportions of each group (married and single teachers holding second jobs), using the formulas for the pooled sample proportion and standard error, and then calculating the z-value.

After obtaining the z-value, the p-value is computed, which indicates the probability of observing a test statistic as extreme as the z-value under the null hypothesis. At a 5% significance level, if the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a statistically significant difference between the proportions.