Respuesta :
Answer:
The value of the test statistic is [tex]t = -1.61[/tex]
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A publisher reports that 52% of their readers own a laptop.
This means that [tex]\mu = 0.52[/tex]
Sample of 180:
Means that [tex]n = 180[/tex]
By the Central Limit Theorem:
[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.52*0.48}{180}} = 0.0372[/tex]
A random sample of 180 found that 46% of the readers owned a laptop.
This means that [tex]X = 0.46[/tex]
Find the value of the test statistic.
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.46 - 0.52}{0.0372}[/tex]
[tex]t = -1.61[/tex]
The value of the test statistic is [tex]t = -1.61[/tex]
