Luna Turner
05/07/2023 · Primary School

Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions \( p_{1} \) and \( p_{2} \) at the level of significance \( \alpha \). Assume that the samples are random and independent. Claim: \( p_{1} \neq p_{2}, \alpha=0.01 \) Sample Statistics: \( x_{1}=32, n_{1}=73, x_{2}=30, n_{2}=83 \) Calculate the standardized test statistic for the difference \( p_{1}-p_{2} \), if applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( z=\square \) B. The conditions to two decimal places as needed.) Calculate the \( P \)-value, if applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( p=\square \) (Round to three decimal places as needed.)

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The conditions for using the normal approximation are satisfied. The standardized test statistic \( z \) is approximately 0.99, and the \( P \)-value is approximately 0.322. Since the \( P \)-value is greater than \( \alpha = 0.01 \), we fail to reject the null hypothesis.

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