A researcher wished to perform a hypothesis test to test the claim that the rate of defectives among the computers of two different manufacturers are the same. She selects two independent random samples and obtains the following sample data.
Manufacturer A: $\mathrm { n } _ { 1 } = 400$, rate of defectives: $1.5 \%$
Manufacturer $B : \mathrm { n } _ { 2 } = 200$, rate of defectives: $3.5 \%$

Can the methods of this section be used to perform a hypothesis test to test for the equality of the two population proportions? Go through the steps of checking whether the conditions for the hypothesis test for two population proportions are satisfied. Show your calculations and state your conclusion.

Question

A researcher wished to perform a hypothesis test to test the claim that the rate of defectives among the computers of two different manufacturers are the same. She selects two independent random samples and obtains the following sample data. 
Manufacturer A: $\mathrm { n } _ { 1 } = 400$, rate of defectives: $1.5 \%$
Manufacturer $B : \mathrm { n } _ { 2 } = 200$, rate of defectives: $3.5 \%$

Can the methods of this section be used to perform a hypothesis test to test for the equality of the two population proportions? Go through the steps of checking whether the conditions for the hypothesis test for two population proportions are satisfied. Show your calculations and state your conclusion.

Quizplus · Accepted Answer

The Answer is

\begin{array} { l } \mathrm { x } _ { 1 } = 400 ( 0.015 ) = 6 \\\mathrm { x } _ { 2 } = 200 ( 0.035 ) = 7 \\\overline { \mathrm { p } } = \frac { 6 + 7 } { 400 + 200 } = 0.0217 \\\mathrm { n } _ { 1 } \overline { \mathrm { p } } = 400 ( 0.0217 ) = 8.7 \\\mathrm { n } _ { 2 } \overline { \mathrm { p } } = 200 ( 0.0217 ) = 4.3\end{array}

Because

\mathrm { n } _ { 2 } \overline { \mathrm { p } } < 5

, the conditions for the hypothesis test are not satisfied.

A Researcher Wished to Perform a Hypothesis Test to Test n1=400\mathrm { n } _ { 1 } = 400n1​=400

A Researcher Wished to Perform a Hypothesis Test to Test $\mathrm { n } _ { 1 } = 400$