One hundred employees working in the construction, manufacturing, and various other industries were selected for review of salary information and educational level. The salaries of the one hundred employees were reviewed to determine if the employees with a bachelor degree or greater earn more than employees with a high school diploma or less. The reviewer claims that at least 70 percent of the 100 employees who have a bachelor degree or greater will have higher salaries. Out of the 100 employees, only fifty of the employees’ salaries will be taken into account. Assume a=0.05.

Question

One hundred employees working in the construction, manufacturing, and various other industries were selected for review of salary information and educational level. The salaries of the one hundred employees were reviewed to determine if the employees with a bachelor degree or greater earn more than employees with a high school diploma or less. The reviewer claims that at least 70 percent of the 100 employees who have a bachelor degree or greater will have higher salaries. Out of the 100 employees, only fifty of the employees’ salaries will be taken into account. Assume a=0.05.

Ho p>- 0.70 proportion of people who have higher salaries with a 4 yr degree or more
H1 p<0.70 proportion of people who do not have higher salaries with a 4 yr degree
perform a 5 step hypothesis test

Answer 1

To perform a 5-step hypothesis test for this scenario, follow these steps:

Step 1: State the null hypothesis (Ho) and alternative hypothesis (H1):
Ho: The proportion (p) of employees with a bachelor's degree or greater who have higher salaries is greater than 0.70.
H1: The proportion (p) of employees with a bachelor's degree or greater who have higher salaries is less than or equal to 0.70.

Step 2: Determine the level of significance (alpha):
Alpha (α) is the threshold used to determine the statistical significance of the test. In this case, α = 0.05, indicating a 5% significance level.

Step 3: Select the test statistic:
Since the sample data includes categorical variables (having a bachelor's degree or greater and higher salary), the appropriate test statistic to use is the one-sample proportion test (also known as a one-sample Z-test).

Step 4: Collect and analyze the data:
In this case, out of the 100 employees, 50 employees' salaries are taken into account.

Step 5: Calculate the test statistic and p-value:
To calculate the test statistic, you need to use the formula for the one-sample Z-test when testing a proportion:

Z = (p̂ - p0) / sqrt(p0 * (1 - p0) / n)

Here,

p̂ is the sample proportion
p0 is the hypothesized proportion under the null hypothesis (0.70)
n is the sample size

Assuming that 70% is p0 = 0.70, you can calculate p̂:
p̂ = 50/100 = 0.50

Now plug in the values and calculate the test statistic (Z) using the formula above.

Once you have the value of Z, you can find the corresponding p-value using a Z-table or a statistical calculator. The p-value will indicate the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

Finally, compare the p-value to the level of significance (α). If the p-value is less than α, you would reject the null hypothesis in favor of the alternative hypothesis. Otherwise, you would fail to reject the null hypothesis.