According to a pew research center study, in may 2011, 38% of all american adults had a smart phone (one which the user can use to read email and surf the internet). a communications professor at a university believes this percentage is higher among community college students. she selects 366 community college students at random and finds that 160 of them have a smart phone. then in testing the hypotheses: h 0 : p = 0.38 versus h a : p > 0.38, what is the test statistic? z = . ( round your answer to two decimal places.)

Step-by-step explanation:

1) Data given and notation

n=366 represent the random sample taken

X=160 represent the people with smartphones

estimated proportion of people with smartphones

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of people with smatrphones is higher than 0.38:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

So the p value obtained was a very low value and using the significance level assumed we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the true proportion of people with smatphones is higher than 0.38.  

395.84

step-by-step explanation:

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