Answer:
a
[tex]N = 222[/tex]
b
[tex]0.36< p <0.44[/tex]
c
No we can not safely conclude that majority of students enjoy statistics because the upper limit of the confidence level is less than 50%
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 555[/tex]
The percentage that enjoyed statistics is [tex]\r p = 40% = 0.40[/tex]
Generally the number of student who say they enjoyed statistics is mathematically represented as
[tex]N = 0.40 * 55[/tex]
=> [tex]N = 222[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = ( 100-95)\%[/tex]
=> [tex]\alpha = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p (1 - \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{ \frac{0.40 (1- 0.40 )}{ 555} }[/tex]
=>. [tex]E = 0.04[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.40 - 0.04 < p <0.40 + 0.04[/tex]
=> [tex]0.36< p <0.44[/tex]
No we can not safely conclude that majority of students enjoy statistics because the upper limit of the confidence level is less than 50%
