Suppose an oil corporation has several thousand drilling sites available in an area of the North Sea. Exploratory wells were drilled in a simple random sample of 50 sites. In 20 of the drilled wells, they found an abundance of oil, and in the remaining 30, they did not. A hypothesis test was conducted to determine if these drillings had a higher success rate than previous exploratory drilling. The success rate of the corporation's prior exploratory drillings was 35%.

Which of the following statements are true? (Select all true statements)

A) Random: The random condition is not met because the sample size is small.

B) 10%: This condition is not met because 20 > 10% of n = 50.

C) 10%: This condition is met because 50 < 10% of all possible sites.

D) Large Counts: This condition is met because $ np_0 = 50(0.35) = 17.5 $ and $ n(1 - p_0) = 50(1 - 0.35) = 32.5 $ are both at least 10.

E) Large Counts: This condition is met because $ np = 20 $ and $ n(1 - \hat{p}) = 30 $ are both at least 10.

F) Random: The random condition is met because the sample is a simple random sample of 50 sites.

The true statements regarding the hypothesis testing conditions for the drilling sites are: F) the random condition is met because it is a simple random sample, C) the 10% condition is met because the sample size is less than 10% of the population, and E) the large counts condition is met as both np and n(1-p) are at least 10.

Explanation:

To analyze the statements provided, we should consider the conditions required for a hypothesis test regarding a population proportion using a sample. Here are the truths among the statements:

F) Random: This condition is met because the sample is a simple random sample of 50 sites. A simple random sample means that every set of drilling sites has an equal chance of being selected, which meets the randomness condition for hypothesis testing.
C) 10%: This condition is met because 50 < 10% of all possible drilling sites. Assuming the total number of drilling sites is in the thousands, the sample of 50 would be far less than 10% of the population, which adheres to the guideline that the sample size should be less than 10% of the population when using the binomial distribution results without needing a finite population correction factor.
E) Large Counts: This condition is met because np = 20 and n(1
- p) = 30 are both at least 10. In a binomial distribution, np and nq (where q = 1-p, and p is the sample proportion) must both be at least 5 to approximate a normal distribution. Since these values are both well above 5, the large counts condition is satisfied.

The other statements A, B, and D are misleading or incorrect based on the information presented.