Q6 **Hypothesis Testing for Proportion****State the appropriate null and alternative hypotheses.**- \( H_0: p = 0.40 \) \( H_a: p < 0.40 \)- \( H_0: p = 0.40 \) \( H_a: p > 0.40 \)- \( H_0: p = 0.40 \) \( H_a: p \neq 0.40 \)**Calculate the test statistic and determine the P-value.**(Round your test statistic to two decimal places and your P-value to four decimal places.)\( z = \_\_\_\_\_\_ \)\( P\text{-value} = \_\_\_\_\_\_ \)**State the conclusion in the problem context.**- Do not reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.- Reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.- Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.- Do not reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.**Would your conclusion have been different if a significance level of 0.05 had been used?**- Yes- No**Explanation of Graphs/Diagrams:**There are no graphs or diagrams included in this document. ### Statistical Analysis of Blood Types in DonationsIn a recent study, a random sample of 164 blood donations was analyzed to determine the distribution of blood types. The findings revealed that 89 of these donations were type A blood. This raises the question: Does the actual percentage of type A blood donations differ from the known population percentage of 40% for type A blood?To answer this question, we will carry out a hypothesis testing procedure using a significance level of 0.01. The hypothesis test will determine if there is a statistically significant difference between the observed proportion of type A blood donations in our sample and the expected proportion in the general population (40%).#### Hypothesis Testing Procedure1. **Null Hypothesis (\(H_0\))**: The actual percentage of type A blood donations is 40%. \[ H_0: p = 0.40 \]2. **Alternative Hypothesis (\(H_A\))**: The actual percentage of type A blood donations is not 40%. \[ H_A: p \neq 0.40 \]3. **Significance Level (\(\alpha\))**: 0.014. **Sample Data**: - Sample Size (\(n\)): 164 - Number of Type A Blood Donations (\(X\)): 895. **Sample Proportion (\(\hat{p}\))** of Type A Blood: \[ \hat{p} = \frac{X}{n} = \frac{89}{164} \]6. **Standard Error (SE)**: \[ SE = \sqrt{\frac{p(1-p)}{n}} \]7. **Test Statistic** (Z-score): \[ Z = \frac{\hat{p} - p}{SE} \]8. **Decision Rule**: Compare the Z-score to critical values from the Z-distribution for a two-tailed test at \(\alpha = 0.01\).This analysis will help determine if the observed proportion of type A blood donations in the sample significantly deviates from the expected 40%, thus providing insights into the blood donation patterns at this blood bank.---By conducting this hypothesis test, we can draw conclusions about the blood donation trends and potentially inform strategies for managing blood donation stocks.

Givenx=89n=164α=0.01p^=xn=89164≅0.5427

A random sample of 164 recent donations at a certain blood bank reveals that 89 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01.