Answer:
Question 5
correct option is A
Question 6
correct option is D
Question 7
correct option is A
Step-by-step explanation:
Considering question 5
From the question we are told that
The population proportion considered is
The sample size is n = 200
The number that had a personal computer at home is ![k = 65](https://tex.z-dn.net/?f=k%20%20%3D%20%2065)
The level of significance is ![\alpha = 0.01](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%200.01)
The null hypothesis is ![H_o : p = 0.25](https://tex.z-dn.net/?f=H_o%20%3A%20%20p%20%3D%20%200.25)
The alternative hypothesis is ![H_a : p > 0.25](https://tex.z-dn.net/?f=H_a%20%3A%20%20p%20%3E%200.25)
Generally from the z-table the critical value of
to the right of the curve is
![z_{\alpha } = 2.33](https://tex.z-dn.net/?f=z_%7B%5Calpha%20%7D%20%3D%20%202.33)
Generally given that it is a right-tailed test , the rejection region is
z > 2.33
Considering question 6
The sample size is n = 20
The standard deviation is ![s = 2](https://tex.z-dn.net/?f=s%20%3D%202)
The sample mean is ![\=x = 6.3](https://tex.z-dn.net/?f=%5C%3Dx%20%20%3D%20%206.3)
The population mean ![\mu = 6.7](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%206.7)
Generally the test statistics is mathematically represented as
![t = \frac{ \= x - \mu }{\frac{s}{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%20%5C%3D%20x%20%20-%20%20%5Cmu%20%20%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D%20%20%7D)
=> ![t = \frac{ 6.3 - 6.7 }{ \frac{ 2}{ \sqrt{20} } }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B%206.3%20-%20%206.7%20%20%7D%7B%20%5Cfrac%7B%202%7D%7B%20%5Csqrt%7B20%7D%20%7D%20%20%7D)
=> ![t = -0.894](https://tex.z-dn.net/?f=t%20%20%3D%20-0.894)
Considering question 7
The sample size is n = 60
The sample mean is ![x = 39](https://tex.z-dn.net/?f=x%20%3D%2039)
The population proportion ![p = 0.85](https://tex.z-dn.net/?f=p%20%3D%200.85)
Gnerally the sample proportion is mathematically represented as
![\^ p = \frac{x}{n}](https://tex.z-dn.net/?f=%5C%5E%20p%20%20%3D%20%20%5Cfrac%7Bx%7D%7Bn%7D)
=>
=>
Generally the standard error of this distribution is mathematically represented as
![SE = \sqrt{ \frac{ p(1 - p ) }{ n } }](https://tex.z-dn.net/?f=SE%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B%20p%281%20-%20p%20%29%20%7D%7B%20n%20%7D%20%7D)
=> ![SE = \sqrt{ \frac{ 0.85 (1 - 0.85 ) }{ 60 } }](https://tex.z-dn.net/?f=SE%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B%20%200.85%20%281%20-%200.85%20%20%29%20%7D%7B%2060%20%20%7D%20%7D)
=> ![SE = 0.0461](https://tex.z-dn.net/?f=SE%20%3D%20%200.0461)
Generally the test statistics is mathematically represented as
![z = \frac{ \^ p - p }{SE}](https://tex.z-dn.net/?f=z%20%20%3D%20%20%5Cfrac%7B%20%5C%5E%20%20p%20%20-%20%20p%20%20%20%7D%7BSE%7D)
=> ![z = \frac{ 0.65 - 0.85 }{0.0461}](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%200.65%20-%200.85%20%20%7D%7B0.0461%7D)
=> ![z = -4.34](https://tex.z-dn.net/?f=z%20%20%3D%20-4.34)