A chemist made six independent measurements of the sublimation point of carbon dioxide (the temperature at which it changes to dry ice). The sample mean was \(196.64 \mathrm{~K}\) with a standard deviation of \(0.68 \mathrm{~K}\).

a. Use the Student's \(t\) distribution to find a \(95 \%\) confidence interval for the sublimation point of carbon dioxide.

b. Use the Student's \(t\) distribution to find a \(98 \%\) confidence interval for the sublimation point of carbon dioxide.

c. If the six measurements had been \(196.35,196.32\), 196.4 198.02, 196.36, 196.39, would the confidence intervals above be valid? Explain.