Answer:
Step-by-step explanation:
Given that:
The sample size = 150
The sample mean = 70.69
The standard deviation = 29.60
The sample mean is equal to the point estimate of the population = 70.69
At 99% confidence interval level is:
∝ = 1 - 0.99
∝ = 0.01
The critical value:
[tex]Z_{\alpha/2} = Z_{0.01/2} \\ \\ Z_{0.005} = 2.58 \ using \ Z \ tables[/tex]
The Margin of error = [tex]Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]= 2.58 \times \dfrac{29.6}{\sqrt{150}}[/tex]
= 2.58 × 2.4168
≅ 6.235
At 99% confidence interval; the estimate of the population mean lies within the interval:
= [tex]\overline x - E < \mu \ < \overline x + E[/tex]
= 70.69 - 6.235 < μ < 70.69 + 6.235
= 64.455 < μ < 76.925
= (64.455 , 76.925 )
