Answer:
[tex]3.5-1.999\frac{0.5}{\sqrt{100}}=3.40[/tex]
[tex]3.5+ 1.999\frac{0.5}{\sqrt{100}}=1.10[/tex]
And the confidence interval for the true mean would be (1.10; 3.40)
Step-by-step explanation:
Information given
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=0.5[/tex] represent the population standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence interval is 0.9544 or 95.44%, the significance would be [tex]\alpha=0.0456[/tex] and [tex]\alpha/2 =0.0228[/tex], and the critical value for this case would be [tex]z_{\alpha/2}=1.999[/tex]
Replacing we got:
[tex]3.5-1.999\frac{0.5}{\sqrt{100}}=3.40[/tex]
[tex]3.5+ 1.999\frac{0.5}{\sqrt{100}}=1.10[/tex]
And the confidence interval for the true mean would be (1.10; 3.40)
