a) Do the data support the claim that reducing the filmthickness increases the m
ID: 2954272 • Letter: A
Question
a) Do the data support the claim that reducing the filmthickness increases the mean speed of the film? Use =0.10 andassume that the two population of film speed is normallydistributed. What is the P-value for this test? b) Find a 90% confidence interval on the difference in the twomeans that can be used to test the claim in part a). A photoconductor film is manufactured at a nominal thicknessof 25 mils. The product engineer wishes to increase the mean speedof the film, and believes that this can be achieved by reducing thethickness of the film to 20 mils. Eight samples of each filmthickness are manufactured in a pilot production process, and thefilm speed ( in microjoules per square inch) is measured. For the25-mil film the sample data result is x1=1.15, s1=0.11, while for the 20-mil film, the data yield x2=1.06, s2=0.09. Note that an increase in film spped would lowerthe value of the observation in microjoules per square inch. a) Do the data support the claim that reducing the filmthickness increases the mean speed of the film? Use ?=0.10 andassume that the two population of film speed is normallydistributed. What is the P-value for this test? b) Find a 90% confidence interval on the difference in the twomeans that can be used to test the claim in part a).Explanation / Answer
a) Do the data support the claim that reducing the filmthickness increases the mean speed of the film? Use =0.10 andassume that the two population of film speed is normallydistributed. What is the P-value for this test?The test hypothesis is
Ho:1<=2
Ha:1>2
The test statistic is
t=(xbar1 - xbar2)/(s1^2/n1 + s2^2/n2)
=(1.15-1.06)/sqrt(0.11^2/8 + 0.09^2/8)
= 1.79
The p-value is P(t(with df=n1+n2-2=14) > 1.79) = 0.0475 (checkstudent t table)
Since p-value is less than =0.1, we reject Ho.
b) Find a 90% confidence interval on the difference in the twomeans that can be used to test the claim in part a).
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