Sebastian wants to estimate the proportion of the sophomores at his high school

Question

Sebastian wants to estimate the proportion of the sophomores at his high school who like to waterski. He interviews a simple random sample of 60 of the 150 sophomores on campus. He finds that 19 like to waterski. Is the independent condition for finding confidence intervals met? Explain.

A. Yes, the independent condition for finding confidence intervals is met because np = 19 and n(1 p) = 41, both of which are at least 10.

B. Yes, the independent condition for finding confidence intervals is met because the sample size is greater than 30.

C. No, the independent condition for finding confidence intervals is not met because np = 19 and n(1 p) = 41, both of which are less than 100.

D. No, the independent condition for finding confidence intervals is not met, because 60 is more than 10% of 150.

E. Yes, the independent condition for finding confidence intervals is met because the sample is a simple random sample.

Explanation / Answer

Here

population size N=150

Sample size n=60

Independance condition: In hypothesis testing, sample should not more than 10% of the population size

Here 10% of 150 is 15.

So independence condition fails here.

Answer is D

D. No,ththe independent condition for finding confidence interval is not met, because 60 ismore than 10% of 150   

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