# Q3a) Using a Confidence Interval to Test a Hypotheis

## SOLUTION

This is an odd question that only rarely appears on exams. You are asked to determine if the mean of a population falls within a specific interval:

19.16mg ± 1 = 18.16mg to 20.16mg

For this reason, we cannot just use the t-test of an unknown population mean. Instead, we must calculate the 99% confidence interval (which deals with intervals), and then see how that interval compares to the claimed interval of 18.16mg to 20.13mg.

If the entire 99% confidence interval falls within this claimed range, it supports the hypothesis that the mean THC level is within 1 mg of 19.16 mg at the 1% significance level.

### Given:

Sample mean: = 19.16 mg

Sample variance: = 0.0330

Sample size: = 19

### Calculations

99% Confidence Interval:

Critical t-value for 99% confidence level with 18 degrees of freedom:

Standard Deviation: mg

Confidence Interval: mg

### Conclusion

We estimate that the mean THC amount falls between 19.0399mg and 19.2801mg, and this type of estimator is correct 99% of the time

Since this interval lies entirely within the range of 18.16 mg to 20.16 mg, we can say there is sufficient evidence (at the 1% significance level) that GH’s product is within 1 mg of 19.16 mg.