Assume that you plan to use a significance level of $\alpha = 0.05$ test the claim that p $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
-$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 140 \
\mathrm { x } _ { 1 } = 41 & \mathrm { x } _ { 2 } = 35
\end{array}$$
A) 0.4211
B) 0.0512
C) 0.0021
D) 0.0086

Question

Assume that you plan to use a significance level of $\alpha = 0.05$ test the claim that p $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 140 \
\mathrm { x } _ { 1 } = 41 & \mathrm { x } _ { 2 } = 35
\end{array}$$
A) 0.4211
B) 0.0512
C) 0.0021
D) 0.0086

Quizplus · Accepted Answer

The P-value for the hypothesis test is 0.0086. This is found by using the chi-square test statistic, which is calculated as:$$\chi^2 = \frac{(x_1 - n_1p)^2}{n_1p} + \frac{(x_2 - n_2p)^2}{n_2p}$$where $x_1$ and $x_2$ are the number of successes in each sample, $n_1$ and $n_2$ are the sample sizes, and $p$ is the hypothesized proportion of successes.In this case, we have:$$\chi^2 = \frac{(41 - 100(0.5))^2}{100(0.5)} + \frac{(35 - 140(0.5))^2}{140(0.5)} = 8.64$$The P-value is then found by using a chi-square distribution table with 1 degree of freedom. The P-value for $\chi^2 = 8.64$ and 1 degree of freedom is 0.0086.

Assume That You Plan to Use a Significance Level Of \alpha