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 [tex]p = 0.25[/tex]
The sample size is n = 200
The number that had a personal computer at home is [tex]k = 65[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : p = 0.25[/tex]
The alternative hypothesis is [tex]H_a : p > 0.25[/tex]
Generally from the z-table the critical value of [tex]\alpha = 0.01[/tex] to the right of the curve is
[tex]z_{\alpha } = 2.33[/tex]
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 [tex]s = 2[/tex]
The sample mean is [tex]\=x = 6.3[/tex]
The population mean [tex]\mu = 6.7[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 6.3 - 6.7 }{ \frac{ 2}{ \sqrt{20} } }[/tex]
=> [tex]t = -0.894[/tex]
Considering question 7
The sample size is n = 60
The sample mean is [tex]x = 39[/tex]
The population proportion [tex]p = 0.85[/tex]
Gnerally the sample proportion is mathematically represented as
[tex]\^ p = \frac{x}{n}[/tex]
=> [tex]\^ p = \frac{39}{60}[/tex]
=> [tex]\^ p = 0.65[/tex]
Generally the standard error of this distribution is mathematically represented as
[tex]SE = \sqrt{ \frac{ p(1 - p ) }{ n } }[/tex]
=> [tex]SE = \sqrt{ \frac{ 0.85 (1 - 0.85 ) }{ 60 } }[/tex]
=> [tex]SE = 0.0461[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \^ p - p }{SE}[/tex]
=> [tex]z = \frac{ 0.65 - 0.85 }{0.0461}[/tex]
=> [tex]z = -4.34[/tex]
