Kris is staining 30 wooden rectangular fence pieces. The fence pieces are different sizes, and Kris wants
to determine the approximate number of square feet of paint she will need. She decides to take a sample
of 4 fence pieces and calculate the mean of the areas instead of calculating the area of each fence piece.
Which is a true statement about this problem?
A. The sample size is 30,
B. The population is the 4 fence pieces
C. The mean area of the 4 fence pieces is a parameter
D. The mean area of the 4 fence pieces multiplied by 30 would be similar to the total area.******
I think D
The correct answer is D, punish if i'm wrong master.
To determine the approximate number of square feet of paint needed, Kris takes a sample of 4 fence pieces and calculates the mean of their areas. Let's analyze each option and find the correct statement:
A. The sample size is 30: This statement is not true because the sample size is given as 4, not 30. Therefore, option A is incorrect.
B. The population is the 4 fence pieces: This statement is true. In this problem, the population being referred to is the entire set of fence pieces, which consists of 30 wooden rectangular pieces. However, Kris is taking a sample of 4 pieces from this population to estimate the mean area. Therefore, option B is correct.
C. The mean area of the 4 fence pieces is a parameter: This statement is not true. Parameters are characteristics of the entire population, not just a sample. The mean area of the 4 fence pieces is a statistic, not a parameter. Therefore, option C is incorrect.
D. The mean area of the 4 fence pieces multiplied by 30 would be similar to the total area: This statement is true. Since the sample is selected randomly from the population, the mean of the sample can be used to estimate the mean of the population. Multiplying the estimated mean area by the total number of fence pieces (30) would provide a reasonable approximation of the total area of all the fence pieces. Therefore, option D is correct.
Hence, the correct statement is D.