Consider $H_{0}: \mu=80$ versus $H_{1}: \mu \neq 80$ for a population that is normally distributed.
a. A random sample of 25 observations taken from this population produced a sample mean of 77 and a standard deviation of 8 . Using $\alpha=.01$, would you reject the null hypothesis?
b. Another random sample of 25 observations taken from the same population produced a sample mean of 86 and a standard deviation of $6 .$ Using $\alpha=.01$, would you reject the null hypothesis?
