Final answer:
The point estimate for the average weight loss is 2.417 pounds, which is an unbiased estimate. The point estimate for the variance and standard deviation can be calculated from the individual weight losses using the respective formulas, taking into account Bessel's correction to ensure that the variance estimate is unbiased.
Step-by-step explanation:
To answer the student's question, we will perform statistical analysis using the provided data on weight loss from an experimental diet. To find the point estimate for the average weight loss, we add up all the individual weight losses and divide by the number of students. This gives us the sample mean, which serves as the point estimate. In this case, we sum the losses in pounds: 2.2 + 2.6 + 0.4 + 2.0 + 0.0 + 1.8 + 5.2 + 3.8 + 4.2 + 3.8 + 1.4 + 2.6 = 29.0 pounds. Since there are 12 students, we divide by 12, yielding a mean loss of 29.0/12 = 2.417 pounds. This is an unbiased estimate of the population mean, as long as the sample is random and representative of the population.
To find the point estimate for the variance, we use the formula for the sample variance, which is computed as the sum of squared differences between each data point and the sample mean, divided by (n - 1), where n is the sample size. This estimation is unbiased, as we are using (n - 1) instead of n in the denominator, which is the Bessel's correction. The point estimate for the standard deviation is simply the square root of the variance. It serves as a measure of how spread out the weight loss values are around the mean.