The 95 percent confidence interval about a mean difference was -3.0 minutes to 6.5 minutes. The null hypothesis that the two population means are equal

To analyze the null hypothesis that the two population means are equal based on the given 95 percent confidence interval, you need to consider whether the interval contains zero. Here's how you can interpret and test the null hypothesis:

1. Understand the 95 percent confidence interval:

A 95 percent confidence interval means that if the same study is conducted multiple times, about 95 percent of the time the calculated confidence intervals will contain the true population mean difference.

In this case, the confidence interval is -3.0 minutes to 6.5 minutes. This suggests that the true population mean difference lies somewhere between -3.0 minutes and 6.5 minutes, with a confidence level of 95 percent.

2. Test the null hypothesis:

The null hypothesis (H0) states that there is no difference between the two population means. In this case, it means the difference in means is zero.

To test the null hypothesis based on the confidence interval, check if the interval contains zero. If it does, you fail to reject the null hypothesis. If it doesn't, you have evidence to reject the null hypothesis.

In this case, since the confidence interval of -3.0 to 6.5 minutes does contain zero, you would fail to reject the null hypothesis. This suggests that there is no statistically significant difference between the two population means. However, it's important to note that this does not prove that the population means are exactly equal, only that there is insufficient evidence to conclude otherwise based on the given data.

Remember, the confidence interval provides an estimate of where the true population mean difference lies, while the hypothesis test determines whether there is enough evidence to support or reject the null hypothesis. The two approaches work together to provide a comprehensive analysis.