Respuesta :
Answer:
[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]
[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]
3.49 < u < 4.37
Step-by-step explanation:
Data provided
3.6, 3.1, 4.0, 4.9, 3.0, 4.3, 3.6, 4.6, 4.6, 4.0, 4.4, 3.6, 3.3, 4.2, 3.7
The sample mean and deviation can be calculated with the following formulas
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex]
[tex]\bar X=3.93[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=0.574 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the true mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=15-1=114[/tex]
The Confidence is 0.99 or 99%, the significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value would be[tex]t_{\alpha/2}=2.977[/tex]
Replacing we got:
[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]
[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]
3.49 < u < 4.37
