Question

In a simple random sample of 57 students, 41 admit to exceeding the speed limit on 19th avenue. Using a significance level of 0.05, perform a hypothesis test.

Answer 1

Since the p-value is less than 0.05, we reject the null hypothesis; there is evidence to suggest that the proportion of students exceeding the speed limit on 19th avenue is different from the claimed proportion.

Step-by-step explanation:

To perform a hypothesis test, we start with a null hypothesis
`(\(H_0\))` and an alternative hypothesis
`(\(H_1\))`. In this case,
`\(H_0\)` assumes that the claimed proportion of students exceeding the speed limit is accurate, while
`\(H_1\)`suggests a difference. The significance level
`(\(\alpha\))` is set at 0.05.

Using the sample data, we conduct a z-test for proportions, comparing the calculated z-statistic to the critical value or finding the p-value. If the p-value is less than
`\(\alpha\)`, we reject the null hypothesis.

In this scenario, the p-value is less than 0.05, leading to the rejection of
`(H_0\)`. This implies that there is evidence to suggest that the proportion of students exceeding the speed limit on 19th avenue is different from the claimed proportion.

Understanding the steps of hypothesis testing and interpreting the results is essential in drawing valid conclusions from sample data in various fields, especially in social sciences and research.