Let me analyze the content of the uploaded image. I will extract the relevant mathematical information and provide the necessary computations and explanations.The uploaded image contains a hypothesis testing problem involving the following parts:

Part 1 of 4

(a) Compute the sample proportion ($\hat{p}$) and round the answer to at least three decimal places.

Part 2 of 4

(b) Are the assumptions for the hypothesis test satisfied?

Part 3 of 4

(c) Test the null hypothesis ($H_0 : p = 0.8$) versus the alternative hypothesis ($H_1 : p \neq 0.8$). Compute the test statistic ($z$) and round the answer to at least two decimal places.

Part 4 of 4

(d) Determine the critical values at the $0.05$ level and decide whether to reject $H_0$.

I will proceed step by step:

Part 1

To compute the sample proportion ($\hat{p}$): $\hat{p} = \frac{\text{number of successes}}{\text{sample size}}$ The problem does not provide the data explicitly in the screenshot. If you can provide this information, I can calculate $\hat{p}$.

Part 2

To determine if the assumptions are satisfied:

• The sample size ($n$) should be large enough so that $np \geq 10$ and $n(1-p) \geq 10$.
• If the image gives $n > 10$ for each category, the assumption holds.

Part 3

To calculate the test statistic: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$ Where:

• $\hat{p}$ = sample proportion
• $p_0 = 0.8$ (null hypothesis proportion)
• $n$ = sample size

Please provide the sample data or values of $n$ and successes for an accurate computation.

Part 4

Critical values for a two-tailed test at $\alpha = 0.05$: $\pm z_{0.025}$ From the z-distribution table, $z_{0.025} = 1.960$.

Decision Rule:

• Reject $H_0$ if $|z| > 1.960$.

Please share the missing numerical details so I can finalize the calculations for all parts.