Question

The article "Irritated by Spam? Get Ready for Spit" (USA Today, November 10,2004 ) predicts that "spit," spam that is delivered via Internet phone lines and cell phones, will be a growing problem as more people turn to web- based phone services. In a poll of 5,500 cell phone users, \(20 \%\) indicated that they had received commercial messages and ads on their cell phones. These data were used to test \(H_{o}: p=0.13\) versus \(H_{a}: p>0.13\) where 0.13 was the proportion reported for the previous year. The null hypothesis was rejected. a. Based on the hypothesis test, what can you conclude about the proportion of cell phone users who received commercial messages and ads on their cell phones in the year the poll was conducted? b. Is it reasonable to say that the data provide strong support for the alternative hypothesis? c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

Short answer

a. Given that the null hypothesis was rejected, one can conclude that the proportion of cell phone users receiving commercial messages and ads has increased from the previous year. b & c. Whether the data provides strong support for the alternative hypothesis or against the null hypothesis depends on the p-value or the significance level of the test, which is not provided in this exercise.

Step-by-step solution

Understanding the research hypotheses

Here, we have two hypotheses given. The null hypothesis (\(H_{0}\)) is \(p=0.13\), i.e., the percentage of people receiving spam calls remains the same as the previous year (13%). The alternative hypothesis (\(H_{a}\)) is \(p>0.13\), i.e., the percentage of people receiving spam calls has increased compared to the previous year.

Analyzing the sample data

In the sample data of 5,500 users, 20% of them reported receiving commercial messages and ads on their cell phones. This percentage is higher than the one stated in the null hypothesis, which is 13%.

Conclusions from the hypothesis test

As the null hypothesis is rejected based on the results of the hypothesis test, one can conclude that the percentage of cell phone users receiving commercial messages has increased from the previous year.

Evaluating the strength of evidence

While it is clear that the data does not support the null hypothesis, whether it provides strong evidence for the alternative hypothesis or against the null hypothesis depends on the significance level of the test, which is not provided in this problem. Usually, a lower p-value (below 0.05 or 0.01) is considered as strong evidence against the null hypothesis and for the alternative hypothesis.