A confidence interval for the population mean tells us which values of mean are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis. Ho:mean =Mo starting with a confidence interval: reject Ho if Mo (mean) is outside the interval and fail to reject if Mo is inside the interval.
The alternative hypothesis is always two-sided, Ha: m doesn't = Mo, because the confidence interval extends in both directions from x (bar over x). A 95% confidence interval leads to a test at the 5% significance level because the interval is wrong 5% of the time. In general, confidence level C leads to a test at significance level a = 1-C.
A 95% confidence interval for a population mean is 31.5 + (bar underneath +) 3.4. Use the method described above to answer these questions.
a) With a two-sided alternative, can you reject the null hypothesis that mean = 34 at the 5% (a = 0.05) significance level? Why?
b) With a two-sided alternative, can you reject the null hypothesis that mean = 35 at the 5% significance level? Why?