A student wants to test her hypothesis she gives each of her students an IO test. She finds that the average IQ score is 115 and the standard deviation for the class is 30. There are 22 students in the class. She also knows that the population average IQ is 100 points.
Ho:p=115
Ha=p>115.
What is the right formula and calculate the test statistics
How about a one-sample t-test? Your sample size is fairly small.
Fill in what you know into the formula to calculate the test statistic.
population mean = 100
sample mean = 115
standard deviation = 30
sample size = 22
I'll let you take it from here.
To calculate the test statistic for this hypothesis test, you can use the formula for a z-test. The z-test statistic is calculated by subtracting the population mean from the sample mean and dividing it by the standard deviation divided by the square root of the sample size.
The formula for the z-test statistic is:
z = (x̄ - μ) / (σ / √n)
Where:
- x̄ is the sample mean (115 in this case)
- μ is the population mean (100 in this case)
- σ is the population standard deviation (30 in this case)
- n is the sample size (22 in this case)
Now, let's calculate the test statistics:
z = (115 - 100) / (30 / √22)
z = 15 / (30 / √22)
z = 15 / (30 / 4.69)
z = 15 / 6.41
z = 2.34 (rounded to two decimal places)
So, the calculated test statistic for this hypothesis test is 2.34.