In 2008 ACT,Inc reported that 74% of 1500 randomly selected college freshman rerurned to college the next year. Estimate the national freshman to sophomore retention rate.
a) Verify below the two condition are met for constructing a confidence interval for the population proportion.
b) What is the value of t a/2or z a/2 for 99% confidence interval
c) What is value of the margin of errorfor your interval?
a) In order to construct a confidence interval for the population proportion, we need to verify two conditions:
1) Random Sampling: The 1500 college freshman must have been randomly selected from the population of college freshman across the nation. This ensures that the sample is representative of the entire population.
2) Sufficient Sample Size: The sample size of 1500 should be large enough to satisfy the minimum requirement for constructing a confidence interval. Generally, a sample size greater than 30 is considered sufficient.
b) The value of tα/2 or zα/2 depends on the desired confidence level. For a 99% confidence interval, we use the z-value (since the sample size is large). The z-value corresponding to a 99% confidence level is approximately 2.576.
c) The margin of error for a confidence interval depends on the standard deviation of the sample and the z-value or t-value. However, since the standard deviation is not provided in the question, we cannot calculate the exact margin of error. The margin of error represents the maximum distance between the sample proportion and the population proportion, while still maintaining the desired confidence level. To calculate the margin of error, you would need to know the standard deviation or use an estimated value.
Please note that without knowing the standard deviation or an estimated value, we cannot calculate the margin of error.