Politicians are interested in knowing the opinions of their constituents on important issues. One administrative assistant to a senator claims that more than 63% of adult women favor stricter gun laws. A recent telephone survey (randomly generated phone numbers were used) of 1026 adults by IBR Polls found that 65.9% of adult women favored stricter gun laws. Test the claim that significantly more than 63% of adult women favor stricter gun laws.
The four conditions which must be met for a one-sample test of a proportion are:
A. The data values must be independent.
B. The data must be collected randomly.
C. The sample size must be less than 10% of the population.
D. We expect at least 10 "successes" and 10 "failures", that is np ≥10 and nq≥10.
Which of these conditions are met for this problem?
A) B and C
B) B and D
C) B, C, and D
D) A, B, C, and D
Is it D?
No, the correct answer is B) B and D.
For a one-sample test of a proportion, the following conditions must be met:
B) The data must be collected randomly: In the problem, it is mentioned that a telephone survey using randomly generated phone numbers was conducted. So, this condition is met.
D) We expect at least 10 "successes" and 10 "failures": For this condition, we need to check if both np ≥10 and nq ≥10. Here, "success" refers to adult women favoring stricter gun laws. As we are specifically looking at the opinions of adult women, the sample size (1026) doesn't have to be less than 10% of the entire population. However, we can check if np ≥10 and nq ≥10 using the proportions given in the problem.
np = 1026 * 0.659 (65.9% expressed support) = 675.234
nq = 1026 * (1-0.659) = 350.766
As both np and nq are greater than 10, this condition is also met.
Hence, the correct answer is B) B and D
No, it is not D. In order to determine which conditions are met for this problem, let's go through each condition one by one.
A) The data values must be independent:
This condition refers to the fact that each observation must be independent of each other. In this case, the survey states that randomly generated phone numbers were used, which suggests that the data values are independent. So, condition A is met.
B) The data must be collected randomly:
The survey states that randomly generated phone numbers were used, indicating that the data was collected randomly. Therefore, condition B is met.
C) The sample size must be less than 10% of the population:
The total number of adult women in the population is not provided in the question, so we cannot verify if the sample size (1026) is less than 10% of the population. Therefore, we cannot determine if condition C is met.
D) We expect at least 10 "successes" and 10 "failures":
In this case, "successes" refer to adult women favoring stricter gun laws. The survey states that 65.9% of adult women favored stricter gun laws, which indicates that there are at least 659 successes in the sample. However, we do not know the exact number of failures, so we cannot determine if condition D is met.
Based on the information given, we can say that conditions A and B are definitely met. It is unclear if conditions C and D are met. Therefore, the correct answer is A) B and C.