For H0: ¦Ð ¡Ü .60 versus H1: ¦Ð > .60, ¦Á = .05, x = 56, n = 80
how do i find the test statistic and p-value?
To find the test statistic and p-value for the given hypothesis test, we will use the formula for the one-sample z-test.
The formula for the test statistic (z) is given by:
z = (x - µ) / (σ / √n)
Where:
- x is the sample mean (56 in this case)
- µ is the null hypothesis mean (.60 in this case)
- σ is the population standard deviation (unknown)
- n is the sample size (80 in this case)
To find the p-value, we need to determine the probability of observing a test statistic as extreme as the one calculated (z) under the null hypothesis.
Here are the steps to find the test statistic and p-value:
1. Calculate the standard error (SE) using the formula:
SE = σ / √n
2. Plug the values into the formula to calculate the test statistic (z):
z = (x - µ) / SE
3. Use the standard normal distribution table or a statistical calculator to find the p-value associated with the calculated test statistic (z).
Note: Since the population standard deviation (σ) is unknown, we will typically use the sample standard deviation (s) as an estimate. However, in this case, we are not given the sample standard deviation, so we cannot calculate it. As a result, we will assume that the population standard deviation is unknown and proceed with the formulas using σ.
Please note that without the actual values for the population standard deviation or the sample standard deviation, it is not possible to find the exact test statistic or p-value. However, I have provided the general process for computing them based on the information given.