The Sampling Distribution of a Sample Mean

First, this section discusses the mean and variance of the sampling distribution of the mean. It also shows how central limit theorem can help to approximate the corresponding sampling distributions. Then, it talks about the properties of the sampling distribution for differences between means by giving the formulas of both mean and variance for the sampling distribution. Using the central limit theorem, it also talks about how to compute the probability of a difference between means being beyond a specified value.

Sampling Distribution of Difference Between Means

Questions

Question 1 out of 4.
Population 1 has a mean of 20 and a variance of 100. Population 2 has a mean of 15 and a variance of 64. You sample 20 scores from Pop 1 and 16 scores from Pop 2. What is the mean of the sampling distribution of the difference between means (Pop 1 - Pop 2)?


Question 2 out of 4.
Population 1 has a mean of 20 and a variance of 100. Population 2 has a mean of 15 and a variance of 64. You sample 20 scores from Pop 1 and 16 scores from Pop 2. What is the variance of the sampling distribution of the difference between means (Pop 1 - Pop 2)?

Question 3 out of 4.
The mean height of 15-year-old boys is 175 cm and the variance is 64. For girls, the mean is 165 and the variance is 64. If 8 boys and 8 girls were sampled, what is the probability that the mean height of the sample of boys would be at least 6 cm higher than the mean height of the sample of girls?


Question 4 out of 4.
The mean time to complete a task is 727 millisecond for 3rd graders and 532 milliseconds for 5th graders. The variances of the two grades are 12,000 for 3rd graders and 10,000 for 5th graders. The times for both grades are normally distributed. You randomly sample 12 3rd graders and 14 5th graders. What is the probability that the mean time of the 3rd graders will exceed the mean time of the 5th graders by 150 msec or more?