Solution Found!
The article “An Automatic Visual System for Marble Tile
Chapter 5, Problem 7E(choose chapter or problem)
The article “An Automatic Visual System for Mar- ble Tile Classification” (L. Carrino, W. Polini, and S. Turchetta, Journal of Engineering Manufacture, 2002:1095–1108) describes a measure for the shade of marble tile in which the amount of light reflected by the tile is measured on a scale of 0–255. A perfectly black tile would reflect no light and measure 0, and a perfectly white tile would measure 255. A sample of nine Mezza Perla tiles were measured, with the following results:
204.999 206.149 202.102 207.048 203.496
206.343 203.496 206.676 205.831
Is it appropriate to use the Student’s t statistic to construct a 95% confidence interval for the mean shade of Mezza Perla tile? If so, construct the confidence interval. If not, explain why not.
Questions & Answers
QUESTION:
The article “An Automatic Visual System for Mar- ble Tile Classification” (L. Carrino, W. Polini, and S. Turchetta, Journal of Engineering Manufacture, 2002:1095–1108) describes a measure for the shade of marble tile in which the amount of light reflected by the tile is measured on a scale of 0–255. A perfectly black tile would reflect no light and measure 0, and a perfectly white tile would measure 255. A sample of nine Mezza Perla tiles were measured, with the following results:
204.999 206.149 202.102 207.048 203.496
206.343 203.496 206.676 205.831
Is it appropriate to use the Student’s t statistic to construct a 95% confidence interval for the mean shade of Mezza Perla tile? If so, construct the confidence interval. If not, explain why not.
ANSWER:Step 1 of 2
It is provided that,
Sample size, n = 9
The data showing the measurements of MezzaPella tile is:
204.999 206.149 202.102 207.048 203.496
206.343 203.496 206.676 205.831
Confidence level = 95%
It is required to construct the 95% confidence interval for the mean shade of MezzaPerla tile.
Yes, it is appropriate to use the Student's t statistic to construct a 95% confidence interval for the mean shade of MezzaPerla tile.
Reason:
1. The population standard deviation is not known.
2. The sample size (n = 9 < 30) is very small.
Hence, it is appropriate to use the Student’s t statistic to construct a 95% confidence interval for the mean shade of MezzaPerla tile.