Quiz 4
The value of a sample statistic will vary from sample to sample.
True
As the sample size (n) increases, the variation in the sampling distribution of the sample means increases.
False
The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?
The sample size must be large (at least 30 observations).
The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normally distributed under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?
The sample size must be large (i.e., n must be greater than or equal to 30).
Assume that we have 60 plots of ground and that we want to select a random sample of 6 plots for an experiment. We use row 8 of a random number table and go from left to right across the row of random numbers: 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 18425 84903 42508 32307 Which 6 plots do we include in our random sample?
plots number: 05 07 18 20 56 60
The Central Limit Theorem is important in statistics, because:
For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population.
Two disadvantages of using the "pulling numbers of a hat" method of obtaining a random sample are (1) that it is not feasible for large populations (e.g., 5 million cows) and (2) it is difficult to get a thorough mixing of the pieces of paper.
True
Assume that a population of rabbit weights has a uniform distribution, instead of a normal distribution. We calculate the mean of 1,000 random samples from this population, where the number of observations in each sample is equal to 50. Would you expect the 1,000 sample means to be normally distributed?
Yes
A population of rabbits has a mean weight of 10 lb and a standard deviation of the weights equal to 2 lb. A rabbit breeder selects 5,000 samples of 64 rabbits each, calculates the mean weight of the rabbits in each of these 5,000 samples, and then graphs the 5,000 sample means. If the population of rabbit weights does not have a normal distribution, would we expect the 5,000 sample means to have a normal distribution?
Yes, according to the Central Limit Theorem
A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb. A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. Regardless of the shape of the distribution of the population of turkey weights, would we expect the sample means to be approximately normally distributed?
Yes, according to the Central Limit Theorem
Suppose that a random sample of 256 measurements is selected from a population with a mean of 50 lb and a variance of 16 lb^2. What is the mean and standard deviation of the sampling distribution of the sample mean?
mean = 50 lb and standard deviation = 0.25 lb
Suppose that a random sample of 625 measurements is selected from a population with a mean µ = 500 lb and a variance σ^2 = 100 lb^2. What is the mean and standard deviation of the sampling distribution of the sample mean?
mean = 500 lb and standard deviation = 0.4 lb
A _______________ is a quantity computed from the observations in a sample.
statistic
A population of cats has a mean weight of 15 lb and a standard deviation of the weights equal to 4 lb. A cat breeder selects a large number of samples of 64 cats each, calculates the mean weight of the cats in each of these samples, and then graphs the sample means. The standard deviation of these sample means is expected to be equal to _______.
0.50 lb