Refer to the nanopillar height data on page 25. Using the \(95 \%\) confidence interval, based on the \(t\) distribution, for the mean nanopillar height

(a) decide whether or not to reject \(H_{0}: \mu=320 \mathrm{~nm}\) in favor of \(H_{1}: \mu eq 320\) at \(\alpha=0.05\);

(b) decide whether or not to reject \(H_{0}: \mu=310 \mathrm{~nm}\) in favor of \(H_{1}: \mu eq 310\) at \(\alpha=0.05\).

(c) What is your decision in part

(b) if \(\alpha=0.02\) ? Explain.

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N Mean StDev SE Mean 5 Z 50 305.580 36.971 5.229 95% CI (295.073, 316.087)