The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.
The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
The alternative hypothesis states that a population parameter is smaller, larger, or different from the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.
In the output, the null and alternative hypotheses help you to verify that you entered the correct value for the hypothesized proportion.
The event is the value in the sample that represents a success. Minitab uses the number of events to calculate the sample proportion, which is an estimate of the population proportion. You can change the value Minitab uses as the event by changing the value order. For more information, go to Change the display order of text values in Minitab output.
The sample size (N) is the total number of observations in the sample.
The sample size affects the confidence interval and the power of the test.
Usually, a larger sample size results in a narrower confidence interval. A larger sample size also gives the test more power to detect a difference. For more information, go to What is power?.
The sample proportion equals the number of events divided by the sample size (N).
The sample proportion is an estimate of the population proportion.
Because the proportion is based on sample data and not on the entire population, it is unlikely that the sample proportion equals the population proportion. To better estimate the population proportion, use the confidence interval.
Confidence interval (CI) and bounds
The confidence interval provides a range of likely values for the population proportion. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population proportion. The percentage of these confidence intervals or bounds that contain the proportion is the confidence level of the interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population proportion.
An upper bound defines a value that the population proportion is likely to be less than. A lower bound defines a value that the population proportion is likely to be greater than.
The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size. For more information, go to Ways to get a more precise confidence interval.
The Z–value is a test statistic for Z–tests that measures the difference between an observed statistic and its hypothesized population parameter in units of standard error.
You must choose Normal approximation as the method for Minitab to calculate the Z–value.
You can compare the Z-value to critical values of the standard normal distribution to determine whether to reject the null hypothesis. However, using the p-value of the test to make the same determination is usually more practical and convenient.
To determine whether to reject the null hypothesis, compare the Z–value to the critical value. The critical value is Z1-α/2 for a two–sided test and Z1-α for a one–sided test. For a two-sided test, if the absolute value of the Z–value is greater than the critical value, you reject the null hypothesis. If it is not, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a standard normal table in most statistics books. For more information, go to Using the inverse cumulative distribution function (ICDF) and click "Use the ICDF to calculate critical values".
The Z-value is used to calculate the p-value.
The p-value is a probability that measures the evidence against the null hypothesis. A smaller p-value provides stronger evidence against the null hypothesis.
Use the p-value to determine whether the population proportion is statistically different from the hypothesized proportion.
To determine whether the difference between the population proportion and the hypothesized proportion is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
P-value ≤ α: The difference between the proportions is statistically significant (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population proportion and the hypothesized proportion is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
P-value > α: The difference between the proportions is not statistically significant (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population proportion and the hypothesized proportion is statistically significant. You should make sure that your test has enough power to detect a difference that is practically significant. For more information, go to Power and Sample Size for 1 Proportion.