Question # $10[10$ pts$]$The fasting blood glucose level of a randomly selected person was measured for seven days, and the following readings were made: $7\mathrm{.}0,7\mathrm{.}7,6\mathrm{.}8,7\mathrm{.}1,7\mathrm{.}1,6\mathrm{.}1,7\mathrm{.}3.$ It is reasonable to ansume the glucose level distribution is normal. A diabetes researcher would like to study the varisbility in the fasting blood glucose level readings for this person. The researcher believes that fasting blse glucose never varies more than $0\mathrm{.}64$ mmol $3/$L$.($a$)$ Test the appropriate hypotheses to determine if the sample data present sufficient evidence to reject the researcher's claim. Use the critical value approach with in e $0\mathrm{.}13($b$)$ What is the approximate p$-$value for the test statistic? Draw your conclusion using a $=0\mathrm{.}05.($c$)$ Estimate the population variance using a $90\%$ confidence interval. Based on this interval, can we infer at the $90\%$ confidence that the population variance is significantly less than $1?$