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 npÌ‚ = 19 and n (1 âˆ' pÌ‚ ) = 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 npÌ‚ = 19 and n (1 âˆ' pÌ‚ ) = 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.

Question

Mathematics

Harley Mahoney

16 April, 06:43

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 npÌ‚ = 19 and n (1 âˆ' pÌ‚ ) = 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 npÌ‚ = 19 and n (1 âˆ' pÌ‚ ) = 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.

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Answers (1)

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Randy Roberts · Answer 1

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

Step-by-step explanation:

We have a sample size of 150.

The proportion of Yes answers is p=60/150=0.6

The proportion of No answers is q=1-0.6=0.4.

The conditions for independence in this case can be said it is satisfied because the sample was chosen randomly.

The other options refer to what is known as the "10% Condition", where the sample size should be less than 10% of the population, and the "sample size condition" for the binomial distribution, where n*p and n*q should be bigger than 10.

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