State your null hypothesis with scientific notation State yo

State your null hypothesis with scientific notation.

State your alternative hypothesis with scientific notation.

Calculate SE.

Calculate CI.

Calculate Z-statistic.

Make a statistical decision: i.e., whether or not to reject the null hypothesis.

Draw your conclusion: i.e., statement regarding the parameter.

1) For a comparison of the rates of defectives produced by two assembly lines, an independent random sample of 100 items is selected from each line. Line A yielded 18 defectives in the sample, and line B yielded 12 defectives. Test whether there is a difference in the defection rates between the two lines with ?=2%.

Solution

State your null hypothesis with scientific notation.

Let p1 be the proportion for Line A

Let p2 be the proportion for Line B

Null hypothesis: p1=p2

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State your alternative hypothesis with scientific notation.

Alternative hypothesis: p1 not equal to p2

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Calculate SE.

SE=sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=sqrt(0.18*(1-0.18)/100+0.12*(1-0.12)/100)

=0.05031898

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Calculate CI.

Given a=0.02, Z(0.01) = 2.33 (from standard normal table)

So the lower bound is

(p1-p2) -Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.18-0.12) -2.33*0.05031898

=-0.05724322

So the upper bound is

(p1-p2) +Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.18-0.12) +2.33*0.05031898

=0.1772432

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Calculate Z-statistic.

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.18-0.12)/0.05031898

=1.19

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Make a statistical decision: i.e., whether or not to reject the null hypothesis.

Since the interval include 0, we do not reject the null hypothesis.

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Draw your conclusion: i.e., statement regarding the parameter.

So we can conclude that p1=p2