Question

A news article suggests that a majority of voters prefer the Democratic candidate. You believe that the actual percentage is smaller. In a survey of 213 voters, 133 stated that they prefer the Democratic candidate. The significance level is set at 0.10. What can be concluded?

a. What type of statistical test should be used for this study?
b. What are the null and alternative hypotheses regarding the population proportion (please enter decimal values)?
c. What is the test statistic (please show your answer to 3 decimal places)?
d. What is the p-value (please show your answer to 4 decimal places)?
e. Should the null hypothesis be rejected or not?
f. What is the final conclusion based on the results of the study?
g. Interpret the p-value in the context of the study. What does it indicate?

Answer 1

To test whether the actual percentage of voters who prefer the Democratic candidate is smaller than what is suggested by the news article, a hypothesis test for population proportion can be used. The null hypothesis is that the population proportion is equal to the suggested percentage, and the alternative hypothesis is that the population proportion is smaller. The test statistic is -0.298 and the p-value is approximately 0.383, so we fail to reject the null hypothesis.

Step-by-step explanation:

To test whether the actual percentage of voters who prefer the Democratic candidate is smaller than what is suggested by the news article, we can use a hypothesis test for a population proportion.

The null hypothesis (H0) is that the population proportion of voters who prefer the Democratic candidate is equal to the suggested percentage. The alternative hypothesis (Ha) is that the population proportion is smaller.

Using the given information, we can calculate the test statistic (z) and the p-value. The test statistic is -0.298 and the p-value is approximately 0.383.

Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the actual percentage of voters who prefer the Democratic candidate is smaller than what is suggested by the news article.

The p-value represents the probability of obtaining a sample proportion as extreme as or more extreme than the one observed, assuming the null hypothesis is true. In this context, it indicates that there is a 38.3% chance of obtaining a sample proportion as different from what is suggested by the news article, if the actual population proportion is equal to the suggested percentage.