Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $p _ { 1 } = p _ { 2 }$ Use the given sample sizes and numbers of successes to find the P -value for the hypothesis test.
$\begin{array} { l l }
n _ { 1 } = 50 & n _ { 2 } = 50 \
x _ { 1 } = 8 & x _ { 2 } = 7
\end{array}$
A) 0.7794
B) 0.3897
C) 0.6103
D) 0.2206

Question

Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $p _ { 1 } = p _ { 2 }$ Use the given sample sizes and numbers of successes to find the  P -value for the hypothesis test.
$\begin{array} { l l } 
n _ { 1 } = 50 & n _ { 2 } = 50 \
x _ { 1 } = 8 & x _ { 2 } = 7
\end{array}$
A)  0.7794 
B)  0.3897 
C)  0.6103 
D)  0.2206

Quizplus · Accepted Answer

The P-value is calculated using a two-proportion z-test. Given the sample sizes and numbers of successes, the P-value reflects the probability of observing the test statistic or something more extreme under the null hypothesis. The calculation involves finding the difference between sample proportions, standard error, and then using the standard normal distribution to find the P-value. In this case, the correct P-value is 0.7794, indicating a high probability of observing the given results (or more extreme) if the null hypothesis that $p_1 = p_2$ is true. This high P-value suggests that there is not enough evidence to reject the null hypothesis at the $\alpha = 0.05$ level.

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