Answer with explanation:
Let p be the proportion of adults have heard of the new electronic reader.
Given claim : The accompanying technology display results from a test of the claim that 38% of adults have heard of the new electronic reader.
i.e. [tex]p=0.38[/tex]
Then , the set of hypothesis will be :-
[tex]H_0: p=0.38\\\\H_a:p\neq0.38[/tex]
Since, the alternative hypothesis is two tailed , so the test is two-tailed test.
Also, it is given that the sample size : [tex]n=1558[/tex]
Number of adults showed that they have heard of a new electronic reader=522
So the sample proportion for adults have heard of the new electronic reader : [tex]\hat{p}=\dfrac{522}{1558}\approx0.34[/tex]
The test statistic for proportion is given by :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\\Rightarrow\ z=\dfrac{0.34-0.38}{\sqrt{\dfrac{0.38(1-0.38)}{1558}}}\\\\\\\Rightarrow\ z=-3.25279036541\approx-3.25[/tex]
By using standard normal distribution table , the P-value for two tailed test corresponds to the obtained z-value =[tex]=0.0011541[/tex]
