Question

In 2010 the Pew Research Center reported that teenagers send on average 50 text messages every day. A researcher suspects this number is out of date, and wishes to determine if teens are sending fewer texts than they used to. A random sample of 25 teens were found to be sending an average of 47.75 texts per day, with a standard deviation of 15. Testing at 10% significance and stating the null and alternative hypothesis, what can the researcher conclude?

Answer 1

Without key statistical values like a t-score or critical value, we cannot conclude whether teens send fewer texts now compared to the 2010 data. A one-sample t-test would be used here, but more information is needed for a conclusive answer.

Step-by-step explanation:

In the given situation, the researcher has a hypothesis that teens are sending fewer texts than they used to, when compared to the 2010 average of 50 texts per day. The null hypothesis (H0) would be that the mean number of texts sent by teenagers is 50 per day (μ = 50), and the alternative hypothesis (Ha) is that the mean number of texts sent by teenagers is less than 50 per day (μ < 50).

To test the hypothesis at a 10% significance level, the researcher would use a one-sample t-test since the sample size is small (n=25). However, the question does not provide sufficient information to complete the statistical test (e.g., the t-score and the critical value), which are essential to making a conclusion regarding the null hypothesis. Without this information or the ability to conduct the t-test based on the provided data, no conclusion can be drawn about whether teenagers are sending fewer texts nowadays compared to the 2010 average.