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
No, although the random and large counts conditions are met, the 10% condition is not met.
Step-by-step 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).
