Final answer:
To test if the population mean is greater than 100, a random sample of 100 data points was collected, yielding a sample mean of 102 and a sample standard deviation of 20. The decision rule for this hypothesis test is to reject the null hypothesis if the test statistic (z-score) is greater than the critical value or if the p-value is less than the chosen level of significance. Without the chosen level of significance or critical value, the specific decision cannot be determined based on the given sample data.
Step-by-step explanation:
In this hypothesis test, we want to test if the population mean is greater than 100. We have a random sample of 100 data points with a sample mean of 102 and a sample standard deviation of 20. To perform the hypothesis test, we need to set up the null and alternative hypotheses and determine the decision rule.
The null hypothesis, denoted as H0, is that the population mean is 100. The alternative hypothesis, denoted as Ha, is that the population mean is greater than 100. Since we are testing against a specific value (100), we can use the z-test with a one-tailed test.
The decision rule for this hypothesis test is to reject the null hypothesis if the test statistic, which is the z-score, is greater than the critical value. The critical value corresponds to the desired level of significance, which is usually denoted as α. If the p-value is less than α, we also reject the null hypothesis.
In this case, since the alternative hypothesis is that the population mean is greater than 100, we would reject the null hypothesis if the z-score is greater than the corresponding critical value. The critical value depends on the chosen level of significance, such as α = 0.05 or α = 0.01. If the p-value is less than the chosen level of significance, we would also reject the null hypothesis.
Based on the sample data provided, with a sample mean of 102 and a sample standard deviation of 20, you can calculate the test statistic (z-score) using the formula:
z = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
After calculating the z-score, you can compare it to the critical value or calculate the p-value to make a decision regarding the null hypothesis. However, without the chosen level of significance or critical value, we cannot determine the specific decision based on the sample data provided.