Answer:
The sample size is 74
Pbar = 0.05
The variance information is needed
Step-by-step explanation:
The population variance , [tex]\sigma^{2} = 484[/tex]
[tex]\sigma = 22[/tex]
Confidence Interval level = 95% = 0.95
Significance Interval = 1 - CI
Significance Interval = 1 - 0.95 = 0.05
Error margin = 5
The critical value = [tex]Z_{\frac{\alpha}{2} } = Z_{0.025}[/tex] = 1.96 (From the z table)
The sample size is given by:
[tex]n \geq (\frac{Z_{\alpha /2} * \sigma}{E} )^{2}[/tex]
[tex]n \geq (\frac{1.96 * 22}{5}) ^{2}[/tex]
[tex]n \geq 74.373\\n \geq 75[/tex]
[tex]\bar{P} = 1 - P[/tex]
Since P = 0.95
[tex]\bar{P} = 1 - 0.95\\\bar{P} = 0.05[/tex]
The variance information is needed in this question when calculating the sample size
