Answer:
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
Step-by-step explanation:
Information given
n=421 represent the random sample taken
[tex]\hat p=0.65[/tex] estimated proportion of adults that would erase all of their personal information online if they could
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic
Hypothesis to test
We want to check if Most adults would erase all of their personal information online if they could, then the system of hypothesis are :
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
From the information given, it is found that the value of the test statistic is z = 6.16.
At the null hypothesis, we test if it is not most adults that would erase all of their personal information online if they could, that is, the proportion is of at most 50%, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, we test if most adults would, that is, if the proportion is greater than 50%.
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
In this problem, the parameters are: [tex]p = 0.5, n = 421, \overline{p} = 0.65[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.65 - 0.5}{\sqrt{\frac{0.5(0.5)}{421}}}[/tex]
[tex]z = 6.16[/tex]
A similar problem is given at https://brainly.com/question/15908206
