3) Find the test statistic for the following proportion: A collection of 500 randomly selected teachers revealed that 61% felt that all students should be required to take algebra in high school.
To find the test statistic for a proportion, you can use the formula:
test statistic = (sample proportion - hypothesized proportion) / standard error
In this case, the sample proportion is 61% (or 0.61), which represents the proportion of teachers who felt that all students should be required to take algebra in high school.
The hypothesized proportion is the proportion we want to test against. You haven't mentioned a specific hypothesized proportion, so let's assume it is 50%. This means we want to test if the proportion of teachers who felt that all students should be required to take algebra in high school is significantly different from 50%.
The standard error can be calculated using the formula:
standard error = sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)
Plugging in the values, we have:
standard error = sqrt((0.50 * (1 - 0.50)) / 500)
standard error = sqrt((0.25) / 500)
standard error = sqrt(0.0005)
standard error ≈ 0.0224
Now we can calculate the test statistic:
test statistic = (0.61 - 0.50) / 0.0224
test statistic ≈ 4.911
The test statistic for this proportion is approximately 4.911.