Question

A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film, and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is x-bar1=1.13 and s1=0.11, while for the 20-mil film, the data yield x-bar2=1.08 and s2=0.09. Note that an increase in film speed would lower the value of the observation in microjoules per square inch.

(a) Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use a=0.10 and assume that the two population variances are equal and the underlying population of film speed is normally distributed. What is the P-value for this test? Round your answer to three decimal places (e.g. 98.765).

The data ___support/do not support___ the claim that reducing the film thickness increases the mean speed of the film. The P-value is _______.

(b) Find a 95% confidence interval on the difference in the two means that can be used to test the claim in part (a). Round your answers to four decimal places (e.g. 98.7654).

_______ <= mu1 - mu2 <= _______

Answer 1

(a)

H0: Null Hypothesis: (Reducing the film thickness does not increase the mean speed of the film)

HA: Alternative Hypothesis: (Reducing the film thickness increases the mean speed of the film)

n1 = 8

1 = 1.13

s1 = 0.11

n2 = 8

2 = 1.08

s2 = 0.09

Pooled standard deviation is given by:

Test Statistic is given by:

t = (1.13 - 1.08)/0.0503

= 0.995

ndf = 8 + 8 - 2 = 14

One Tail - Right Side Test

By Technology, p - value = 0.168

So,

Answer is:

The data do not support the claim that reducing the film thickness increases the mean speed of the film. The P-value is 0.168.

(b)

= 0.05

From Table, critical values of t = 2.1448

Confidence Interval:

(1.13 - 1.08) (2.1448 X 0.0503)

= 0.05 0.1079

= (- 0.0579 ,0.1579)

Confidence Interval:

- 0.0579 <   < 0.1579