Question

A student would like to estimate the proportion of the senior class that plans to attend prom this year. The student goes to the guidance office and gets a list of the names of all 274 seniors. Using the list, she selects a simple random sample of 50 students and finds that 76% of the selected students plan to attend prom this year. She would like to construct a 95% confidence interval for the proportion of the entire senior class that plans to attend prom this year. Are the conditions for inference met

Answer 1

No, although the random and large counts conditions are met, the 10% condition is not met.

Explanation:

The random condition is met because the student selects a random sample of 50 seniors. The large counts condition is met because there are 38 expected successes and 12 expected failures, which are both at least 10. The 10% condition is not met because n = 50 is not less than 10% of the size of the population (N = 274 seniors).