Final answer:
The best point estimate for the population mean is the sample mean, 3.4. A 99% confidence interval is constructed using the sample mean, sample standard deviation, and the appropriate t-value. The null and alternative hypotheses for testing the true population mean are defined as equals to or not equal to the sample mean, respectively.
Step-by-step explanation:
The best point estimate for the population mean is the sample mean, which in this case is 3.4 points for providing feedback. To construct a 99% confidence interval for the true population mean, we use the t-distribution because the sample size is less than 30. The formula for the confidence interval is given by = sample mean ± (t-value * (sample standard deviation/sqrt(sample size))). With a sample size of 26 and a standard deviation of 1.5, and using the t-distribution table for a degree of freedom of 25 (n-1) at the 99% confidence level, we can find the appropriate t-value. To set up the hypotheses for testing, we can state that the null hypothesis (H0) would be that the population mean is equal to the sample mean (μ = 3.4) and the alternative hypothesis (H1) would be that the population mean is not equal to 3.4 (μ ≠ 3.4). Once the appropriate t-value is found, plug it into the formula to get the confidence interval. For example, if the t-value is 2.796, the confidence interval would be 3.4 ± (2.796 * (1.5/sqrt(26))), which would need to be calculated to get the confidence interval range.