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The shade of marble tile is measured by the amount of light reflected by the tile measured on a scale of 0-255. A perfectly black tile would reflect no light 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
(b) can you conclude that the mean shade of Mezza Perla tile (µ) is greater than 204.8?

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Answer:

Step-by-step explanation:

Sample data

204.999 206.149 202.102 207.048 203.496 206.343 203.496 206.676 205.831

N=9

Sum, Σx: 1846.14

Mean, μ: 205.12666666667

Variance, s^2:  2.6217475555555

Std dev = s = 1.619

The sample mean follows a t distribtion with df =8

Mean difference = 205.13-204.8 = 0.50

Std error = std dev/sqrt n = 0.540

Test statistic = Mean diff/se = 0.9259

p value = 0.1907 (one tailed at 95%)

Since p >0.05 we accept null hypothesis.

We cannot conclude that  the mean shade of Mezza Perla tile (µ) is greater than 204.8

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