Question

In a survey, 400 parents were asked about the importance of sports for boys and girls. Of the parents interviewed, 70% agreed that boys and girls should have equal opportunities to participate in sports. (a) Describe the sampling distribution of the sample proportion of parents who agree that boys and girls should have equal opportunities. (b) Suppose someone claims that the proportion of parents in the population is actually equal to 0.65. What is the probability of observing a sample proportion as large as or larger than the observed value p=0.70?

Answer 1

The sampling distribution of the sample proportion is approximately normal. The probability of observing a sample proportion as large as or larger than 0.70 can be calculated using the sampling distribution and finding the area under the curve beyond 0.70.

Step-by-step explanation:

(a) The sampling distribution of the sample proportion is approximately normal with a mean equal to the true population proportion, which in this case is 0.70, and a standard deviation equal to the square root of (p * (1-p) / n), where p is the population proportion and n is the sample size.

(b) To calculate the probability of observing a sample proportion as large as or larger than p=0.70, we can use the sampling distribution and find the area under the curve beyond 0.70. This can be done using a statistical software or a Z-table. The calculated probability is the p-value, which indicates the likelihood of observing a result as extreme or more extreme than the observed value under the assumption that the proportion is actually 0.65.