Question

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95.44 percent of the sample means for male students.

Answer 1

Answer:

$3.5-1.999\frac{0.5}{\sqrt{100}}=3.40$    

$3.5+ 1.999\frac{0.5}{\sqrt{100}}=1.10$    

And the confidence interval for the true mean would be (1.10; 3.40)

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=0.5$ 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:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$   (1)

The Confidence interval is 0.9544 or 95.44%, the significance would be $\alpha=0.0456$ and $\alpha/2 =0.0228$, and the critical value for this case would be $z_{\alpha/2}=1.999$

Replacing we got:

$3.5-1.999\frac{0.5}{\sqrt{100}}=3.40$    

$3.5+ 1.999\frac{0.5}{\sqrt{100}}=1.10$    

And the confidence interval for the true mean would be (1.10; 3.40)