To determine whether themean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy program tests:
Ho: mu = 1.4
Ha: mu > 1.4
The calculated value of the test statistic is z = 2.42.
==> How do I calculate the p-value from just this z-statistic? Thanks for your help!
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
I didn't realize how simple that was x) thanks so much!
To calculate the p-value from the given z-statistic, you can use a standard normal distribution table or a statistical software.
Here are the steps to calculate the p-value:
1. State the null and alternative hypotheses (already provided):
Ho: mu = 1.4 (the mean nicotine content is equal to 1.4 milligrams)
Ha: mu > 1.4 (the mean nicotine content is greater than 1.4 milligrams)
2. Determine the significance level (alpha). Let's assume alpha is 0.05 (commonly used value).
3. Determine the critical value corresponding to the significance level. Since the alternative hypothesis is one-sided (mu > 1.4), you need to find the critical value for the right tail of the distribution. Looking up the critical value in the standard normal distribution table for a significance level of 0.05, you would find a critical value of approximately 1.645.
4. Compare the calculated test statistic (z = 2.42) with the critical value obtained in step 3. Since the test statistic (2.42) is greater than the critical value (1.645), it falls into the rejection region.
5. Calculate the p-value: The p-value is the probability of observing a test statistic as extreme as the one obtained (z = 2.42) or more extreme, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (mu > 1.4), the p-value corresponds to the area in the right tail of the standard normal distribution beyond the test statistic.
6. Using either a standard normal distribution table or a statistical software, find the probability associated with the test statistic of z = 2.42. The p-value calculated for a z-statistic of 2.42 is approximately 0.0088.
Therefore, the p-value is approximately 0.0088.