A recent report states that less than 50% of the teenagers in Dover City were ab

Question

A recent report states that less than 50% of the teenagers in Dover City were able to pass a driving test. Consequently, the city's driver's education department is trying to convince the city council to fund more driving programs. The council will fund more programs only if the driver's education department can provide convincing evidence that the report is true.

Members of the department plan to collect data from a sample of 150 teenagers who live in Dover City. A test of significance will be conducted at a significance level of = 0.05 for the hypotheses H0: p = 0.50 and Ha: p < 0.50, where p is the proportion of teen residents who live in the city and are able to pass the driving test.

Part A: Describe a Type II error in the context of the study and the consequence of making this type of error. (3 points)

Part B: Members of the driver's education department recruit 150 teenage residents who volunteer to take the driving test. The test is passed by 77 of the 150 volunteers, resulting in a p-value of 0.6280 for the given hypotheses. If it is reasonable to conduct a test of significance for the given hypotheses using the data collected from the 150 volunteers, what does the p-value of 0.6280 lead you to conclude? (4 points)

Part C: Describe the primary flaw in the study described in part B and explain why it is a concern

Explanation / Answer

Result:

A recent report states that less than 50% of the teenagers in Dover City were able to pass a driving test. Consequently, the city's driver's education department is trying to convince the city council to fund more driving programs. The council will fund more programs only if the driver's education department can provide convincing evidence that the report is true.

Members of the department plan to collect data from a sample of 150 teenagers who live in Dover City. A test of significance will be conducted at a significance level of = 0.05 for the hypotheses H0: p = 0.50 and Ha: p < 0.50, where p is the proportion of teen residents who live in the city and are able to pass the driving test.

Part A: Describe a Type II error in the context of the study and the consequence of making this type of error. (3 points)

When the null hypothesis is false and we fail to reject it, we make a type II error.

We fail to reject the null hypothesis of the proportion of teen residents who live in the city and are able to pass the driving test is equal to 0.5 where the true proportion of teen residents who live in the city and are able to pass the driving test is less than 0.5.

Part B: Members of the driver's education department recruit 150 teenage residents who volunteer to take the driving test. The test is passed by 77 of the 150 volunteers, resulting in a p-value of 0.6280 for the given hypotheses. If it is reasonable to conduct a test of significance for the given hypotheses using the data collected from the 150 volunteers, what does the p-value of 0.6280 lead you to conclude? (4 points)

The p-value of 0.6280 is > 0.05 level of significance, we fail to reject the null hypothesis. There is not enough evidence to conclude that true proportion of teen residents who live in the city and are able to pass the driving test is less than 0.5.

Part C: Describe the primary flaw in the study described in part B and explain why it is a concern

Since the sample is not random, we can not generalize the statistical conclusions to the population.

Basic statistical inference based on the assumption that a population sample is a random and representative of the population. If subjects are voluntary, then you cannot be sure that a voluntary patient is truly representative of the population. The samples must be representative in order to generalize statistical conclusions.

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