URGENT HELP NEEDED... Statistics M/C questions

Question

1: To estimate the average SAT score of incoming freshmen, the Admissions office collected the scores of fifty randomly chosen students. From previous years, they know that the population standard deviation will be 27.5. Should they use a z-interval or a t-interval, or do they not have enough information to use either?

 A. They should use a z-interval

 B. They should use a t-interval

 C. They do not have enough information to use either

2: The Admissions office collected the SAT scores of fifty randomly chosen students, from which they found a standard deviation of 27.5. If they wish to construct a 95% confidence interval for the average score for all students, should they use a z-interval or a t-interval, or do they not have enough information to use either?

 A. They should use a z-interval

 B. They should use a t-interval

 C. They do not have enough information to use either

3: The Admissions office collected the SAT scores of twenty randomly chosen students, from which they found a standard deviation of 27.5. If they wish to construct a 95% confidence interval for the average score for all students, should they use a z-interval or a t-interval, or do they not have enough information to use either?

 A. They should use a z-interval

 B. They do not have enough information to use either

 C. They should use a t-interval



Answer 1

Question1: Since you have an n=50, and you have a decent estimate of the standard deviation, you can assume the 'law of large numbers' applies, and use the z-test.

Question 2: for the same reasons as Q#1 AND because you used a z-test, you should provide a z-interval. You should always provide the interval of the test you use.

Question 3: With an n=20, you don't have a large enough sample to use the 'law of large numbers', so you should use a t-interval.

NOTE: a rule of thumb is an n≥30 is large enough to apply the 'Law of large numbers", which basically says as your sample size increases, it becomes closer, and can be approximated by the normal distribution (z).