Question

A camera film is currently manufactured to a thickness of 25 thousandths. The process engineer wants to increase the speed of the film and believes that this can be achieved by decreasing the film thickness to 20 thousandths. Film speed is measured in µJ / in2, which is a measure inversely proportional to speed, that is, at higher speed minus µJ / in2

8 sheets of each thickness are taken (25 mils and 20 mils) and the following results are obtained:

For 25 mils: x-bar = 1.15 µJ / in2 and s = 0.11 µJ / in2

For 20 mils: x-bar = 1.06 µJ / in2 and s = 0.09 µJ / in2

a) Is there evidence to support the belief of the process engineer? (Assume that σ1 = σ2)

Clearly define the hypothesis, the areas of acceptance and rejection, the test statistic and express your conclusion in complete sentence
b) Calculate the P-value for this test

c) Is the presumption of equal variances supported?

Answer 1

(a) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ > µ₂

s2p = (8 - 1)*0.11^2 + (8 - 1)*0.09^2/(8 + 8 - 2) = 0.0101

df = 8 + 8 - 2 = 14

The critical region is:

Reject Ho if t > 1.76.

The test statistic, t = (1.15 - 1.06)/0.0101*(1/8 + 1/8) = 1.791

Since 1.791 > 1.76, we can reject the null hypothesis.

Therefore, we can conclude that decreasing the film thickness to 20 thousandths increases the speed of the film.

(b) The p-value is 0.0475.

Since the p-value (0.0475) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that decreasing the film thickness to 20 thousandths increases the speed of the film.

(c) Ratio of standard deviations = 0.11/0.09 = 1.22 < 2

Since the ratio is less than 2, the presumption of equal variances is supported.

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