Question

Experts believe that 70% of adults in the United States believe it is more enjoyable to be married than single. An ABC News Poll in 2004 surveyed 1,501 randomly selected adults in the United States and asked if they believed it is more enjoyable to be married or single. In the survey, 1,126 people responded that it is more enjoyable to be married. Suppose another 1051 random selected U.S. adults were surveyed and asked if they believed it is more enjoyable to be married or single. The sample proportion who respond that it is more enjoyable to be married from this new sample would most likely be different from the same sample proportion from the old sample due to ___________________.

Answer 1

Due to;

Sampling variability

Explanation:

From the question, we have;

The percentage adults experts believe are convinced that it is more enjoyable to be married than single = 70%

The number of adults in the sample of the survey = 1,501 adults

The number of adults that responded that it is more enjoyable to be married than single = 1,126

According to the central limit theorem, the differences in the two samples and the small sizes of the samples compared to the population, the sample means is different from the population mean, therefore, the sample proportion that respond that it is more enjoyable to be married from the new sample will be different from the old sample due sampling variability because as the sample size is so small compared to the population, some samples can contain more of one category in the population than other samples leading to varying proportion