Please help me solve and come to the complete answer please Hint (complete answer) Thank you!

Question

Simone read online that the failure rate in Arizona for the first attempt of the written driver’s test is 60%. Simone thinks the Arizona rate is less than 60%. To investigate, she selects an SRS of 50 Arizona drivers and finds that 27 failed their first written driving test. To determine if this provides convincing evidence that the failure rate for Arizona is less than 60%, 200 trials of a simulation are conducted. Simone’s hypotheses are: H₀: p = 60% and H_a: p < 60%, where p = the true proportion of Arizona drivers who fail the first attempt of the written driver’s test. Based on the results of the simulation, the estimated P-value of this test is 0.035.

Using a = 0.05, what conclusion should Simone reach?

A.Because the P-value of 0.035 < a, Simone should reject H₀. There is convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

B. Because the P-value of 0.035 < a, Simone should reject H₀. There is not convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

C.Because the P-value of 0.035 < a, Simone should fail to reject H₀. There is convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

D .Because the P-value of 0.035 < a, Simone should fail to reject H₀. There is not convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

Answer 1

Based on the given information, using a significance level of 0.05, Simone should reject the null hypothesis (H0) because the P-value of 0.035 is less than the significance level. Therefore, the correct answer is A: Because the P-value of 0.035 < a, Simone should reject H0. There is convincing evidence that the Arizona written driver’s test has a true first-attempt failure rate less than 60%.

In hypothesis testing, the null hypothesis (H0) is the statement that there is no significant difference or relationship between the variables being tested. In this case, the null hypothesis is that the proportion of Arizona drivers who fail the first attempt of the written driver’s test is 60%.

The alternative hypothesis (Ha) is the statement that there is a significant difference or relationship between the variables being tested. In this case, the alternative hypothesis is that the proportion of Arizona drivers who fail the first attempt of the written driver’s test is less than 60%.

To test the null hypothesis, Simone takes a sample of 50 Arizona drivers and finds that 27 of them failed their first written driving test. She then conducts 200 trials of a simulation to determine the probability of observing a sample proportion as extreme as or more extreme than the observed proportion of 27/50, assuming that the null hypothesis is true. This probability is known as the P-value.

Simone then compares the P-value to her chosen significance level, which is 0.05. If the P-value is less than the significance level, she rejects the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than the significance level, she fails to reject the null hypothesis.

In this case, the P-value is 0.035, which is less than the significance level of 0.05. Therefore, Simone rejects the null hypothesis and concludes that there is convincing evidence that the proportion of Arizona drivers who fail the first attempt of the written driver’s test is less than 60%.