The Pew Internet and American Life Project report that American adults send a mean of 10 text messages per day. A random sample of 100 American adults showed a mean of 12 text messages per day with a standard deviation of 20. Test using level of significance whether the populations mean number of text messages per day differs from 10. Assume the requirements are met. Use the P-value method of testing hypothesis.

Step-by-step explanation:

American adults send a mean of 10 text messages per day.

Claim: whether the populations mean number of text messages per day differs from 10.

Null: u = 10

Alternative: u = / 10

Using the z test where

z = (x - u) / (s/√n)

Where x = 12, u = 10, s = 20 and n = 100

z = (12-10) / (20 / √100)

z = (2) / (20/10)

z = 2/2

z = 1

Assuming significant level of 0.05 for acts tailed test, the p value using the p value calculator from z score is 0.3173 which is greater than 0.05. Thus, we can conclude that there is not enough statistics evidence to prove that populations mean number of text messages per day differs from 10.