Next, you can use your z-table or the p–z converter to find the probability of obtaining a z-value this large or larger, assuming that we are sampling from a normal distribution with a mean of 500. This p-value corresponds to the probability of obtaining a sample mean of 530 or larger from a sample of 10 people randomly selected from a normally distributed population with a mean of 500.
What is the probability of a z score of .95 or more?
p = 0.050
Incorrect! We set the alpha level to .05. If our p-value is less than .05 we will reject the null hypothesis. The p-value corresponds to the area of the z distribution that is greater than our observedz-value. You can use the p-z converter to find this value.
p = 0.171
Correct! The probability of observing a z-score equal to .95 or greater is .171. If the null hypothesis is true such that the training program has no effect, the probability is .171 that the mean for a random sample of 10 graduates is 530 or greater.
p = 0.329
Incorrect! The probability of observing a z-score between zero and .95 is .329. We wish to know the probability of observing a z-score as large or larger than .95.
p = 0.342
Incorrect! The probability of observing a z-score .95 or farther from the mean is .342. This is a two-tailed probability. In our application we are interested only in the upper tail of the distribution.
p = 0.829
Incorrect! The probability of observing a z-score less than or equal to .95 is .829. We would like to know the probability of observing a z-score greater than or equal to .95.