A Simple Random Sample of 10 Houses in a Particular $7.7$

Essay

A simple random sample of 10 houses in a particular town was selected and the level of radon gas measured for each house in the sample. The sample mean was $7.7$ parts per million, and the standard deviation $2.98$ parts per million. Experience has shown that radon gas level is approximately normally distributed in similar populations.
a) Construct and interpret a $99 \%$ confidence interval for $\mu$ .
b) The city standards for radon call for a radon level of no more than $6 \mathrm { ppm }$ . Based on your answer to part (a), does it appear that the mean radon level for city houses is greater than 6 ppm? Provide statistical justification for your response.