Tests the claim that pi < p2. Assume the samples are random and independent. E1 = 44; 2 = 29 %3D n1 = 65 ; n2 = 39 %3D a. Complete the table (use reduced fractions) P1 P2 b. Calculate the Z-test statistic using the standard error from part a. Z = (use 2 decimal places) C. At a = 0.05, Use the distribution table to find the critical values for the rejection region Z. =

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**Testing the Claim that \( p_1 < p_2 \):**

Assume the samples are random and independent.

\[
\bar{x}_1 = 44; \quad \bar{x}_2 = 29
\]

\[
n_1 = 65; \quad n_2 = 39
\]

**a. Complete the table (use reduced fractions):**

\[
\begin{array}{|c|c|c|c|}
\hline
\hat{p}_1 & \hat{p}_2 & \hat{p} & \hat{q} \\
\hline
\text{[Blank]} & \text{[Blank]} & \text{[Blank]} & \text{[Blank]} \\
\hline
\end{array}
\]

**b. Calculate the Z-test statistic using the standard error from part a.**

\( Z = \_\_\_ \) (use 2 decimal places)

**c. At \( \alpha = 0.05 \), use the distribution table to find the critical values for the rejection region.**

\( Z_c = \_\_\_ \)

**d. What is your conclusion?**

- \( \circ \) Accept the alternative hypothesis and reject the claim.
- \( \circ \) Accept the null hypothesis and support the claim.
- \( \circ \) Reject the alternative hypothesis and support the claim.
- \( \circ \) Fail to reject the null hypothesis and do not support the claim.
- \( \circ \) Reject the null hypothesis and support the claim.
Transcribed Image Text:**Testing the Claim that \( p_1 < p_2 \):** Assume the samples are random and independent. \[ \bar{x}_1 = 44; \quad \bar{x}_2 = 29 \] \[ n_1 = 65; \quad n_2 = 39 \] **a. Complete the table (use reduced fractions):** \[ \begin{array}{|c|c|c|c|} \hline \hat{p}_1 & \hat{p}_2 & \hat{p} & \hat{q} \\ \hline \text{[Blank]} & \text{[Blank]} & \text{[Blank]} & \text{[Blank]} \\ \hline \end{array} \] **b. Calculate the Z-test statistic using the standard error from part a.** \( Z = \_\_\_ \) (use 2 decimal places) **c. At \( \alpha = 0.05 \), use the distribution table to find the critical values for the rejection region.** \( Z_c = \_\_\_ \) **d. What is your conclusion?** - \( \circ \) Accept the alternative hypothesis and reject the claim. - \( \circ \) Accept the null hypothesis and support the claim. - \( \circ \) Reject the alternative hypothesis and support the claim. - \( \circ \) Fail to reject the null hypothesis and do not support the claim. - \( \circ \) Reject the null hypothesis and support the claim.
Expert Solution
Step 1

Given that 

n1=65 , x1=44

n2=39 , x2=29

Alpha=0.05

H0:p1=p2  Vs   H1:p1<p2

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