Question

Sample 1 sample 2

sample mean 45 42
sample variance 85 90
sample size 10 12
the point estimate for the difference between the means of the two populations is ?
a. 0
b. 2
c. 3
d. 15

Answer 1

The point estimate for the difference between the populations' means is the difference between the two sample means, which is 3. For reference examples, use normal distribution and t-distribution methods for probability and hypothesis testing respectively, and calculate confidence intervals with given sample means and error bounds.

Step-by-step explanation:

The point estimate for the difference between the means of two populations is simply the difference between the sample means of these populations. Given the means of sample 1 and sample 2 are 45 and 42, respectively, we can calculate the point estimate as follows:

Point Estimate = Sample Mean of Sample 1 - Sample Mean of Sample 2

Point Estimate = 45 - 42 = 3

This calculation gives us the point estimate for the difference between the population means, which in this case is 3. Therefore, the correct answer to the student's question is c. 3.

Now, concerning the provided reference questions:

1. To find the probability that the sample mean is between 85 and 92 for a normally distributed population with a mean of 90 and a standard deviation of 15, with samples of size 25:
2. For a population mean of 13 with a sample mean of 12.8, a sample standard deviation of 2, and a sample size of 20, you would use the t-distribution for a hypothesis test assuming the underlying population is normal.
3. The confidence interval for a sample mean of 15 with an error bound of 3.2 will be 15 ± 3.2.