Question

Please respond to parts 1 AND 2 Surveys have become an integral part of our lives. They directly affect us in so many ways, including public policy, the television shows we watch, the products we buy, and the political leaders we elect. Because it is so important that every citizen has the ability to interpret survey results, we focus on surveys for this discussion. In a recent Pew Research Center poll, 1501 adults were randomly selected and asked this question, " From what you've read and heard, is there solid evidence that the average temperature on earth has been increasing over the past few decades, or not? Seventy percent of the 1501 respondents answered "yes."

1. Would it or would it not be okay for the newspaper to make this statement: "Based on results from a recent survey, the majority of adults believe that there is solid evidence of global warming."

2. A common criticism of surveys is that they poll only a very small percentage of the population and therefore cannot be accurate. Is a sample of only 1501 adults a sample size that is too small? Write a brief explanation of why the sample size of 1501 is or is not too small.

Answer 1

1)

Let the proportion, p = number of people say yes

To test whether there is significant difference in results from survey, the z test for the one proportion is used since the sample data values satisfy the normality condition

The null and alternative hypotheses are defined as,

The z-statistic is obtained using the formula,

The p-value is obtained from z-distribution table for z = 15.4971

Since the P-value is 0.0000<0.01 at 1% significant level, hence the newspaper can make this statement.

2)

Since the sample size of 1501 is greater than 30 to perform the statistical test and surely less than 10% of the population, i.e. the sample follows the 10% rule such that sample size is 10% or less of the population (10% rule) when sampling is being done without replacement. Hence we can conclude that sample size of 1501 is not too small.