## The Pew Research Center reported that 73% of Americans who own a cell phone also use text messaging. In a recent local survey, 155 out of 20

The Pew Research Center reported that 73% of Americans who own a cell phone also use text messaging. In a recent local survey, 155 out of 200 cell phone owners used text messaging.

Since a Z test is appropriate, test whether the population proportion of Americans who use text messaging is different from 73%. Use level of significance α = 0.10.

Hint: Do you need to conduct a t-test or a z-test? Next, find the p-value, using p-value, and level of significance, you can see if the decision (Reject or Do Not reject H0.) You can also find the critical value(s) to finalize your decision.

## Answers ( )

Answer:Now we can find the p value. Since we have a bilateral test the p value would be:

Since the p value is higher than the significance level of 0.1 we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

Do Not reject H0

Step-by-step explanation:Information providedn=200 represent the sample size slected

X=155 represent the cell phone owners used text messaging

estimated proportion of cell phone owners used text messaging

is the value to verify

represent the significance level

We need to conduct a z test for a proportion

z would represent the statistic

represent the p value

System of hypothesisWe want to verify if the true proportion of cell phone owners used text messaging is different from 0.73 so then the system of hypothesis are:

Null hypothesis:

Alternative hypothesis:

The statistic to check this hypothesis is given by:

(1)

Replacing the data given we got:

Now we can find the p value. Since we have a bilateral test the p value would be:

Since the p value is higher than the significance level of 0.1 we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case would be:

Do Not reject H0