The fasting blood glucose level of a randomly selected person was measured for seven days and the following readings were made: 7.0, 7.7, 6.8, 7.1, 7.1, 6.1, 7.3. It is reasonable to assume that the glucose level distribution is normal. A diabetes researcher would like to study the variability in the fasting blood glucose level readings for the selected person. The researcher believes that fasting blood glucose never varies more than 0.8 mmol/L. It is of interest to determine if the sample data present sufficient evidence to reject the researcher's claim.

a. State the appropriate null and alternative hypotheses.

b. What is the appropriate conclusion at the 0.05 level of significance?

c. What is the approximate p-value for the test statistic?

d. Estimate the population variance using a 90% confidence interval.

e. Can we infer at the 90% confidence that the population variance is significantly less than 1?