In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval? A. There is a 95% probability that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

B. We can be 95% confident that the proportion of the sample who use text messaging is between 73.1% and 76.9%.

C. 95% of samples will have between 73.1% and 76.9% of respondents who use text messaging.

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

Question

Alex Bradley

Mathematics

6 May, 11:28

In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval? A. There is a 95% probability that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

B. We can be 95% confident that the proportion of the sample who use text messaging is between 73.1% and 76.9%.

C. 95% of samples will have between 73.1% and 76.9% of respondents who use text messaging.

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

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Answers (1)

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Miranda · Answer 1

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

Step-by-step explanation:

The interpretation of a confidence interval of level x% means that we are x% sure that the interval contains the true mean of the population.

In this problem, we have that:

The population are all the cell phone users.

The 95% confidence interval is (73.1%, 76.9%).

Which of the following is an appropriate interpretation of the 95% confidence interval?

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.