Answer :
Answer:
[tex]44.7-2.052\frac{6.96}{\sqrt{28}}=42.001[/tex]
[tex]44.7+2.052\frac{6.96}{\sqrt{28}}=47.399[/tex]
And the confidence interval would be between 42.001 and 47.399
Step-by-step explanation:
Information given
[tex]\bar X=44.7[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=6.96 represent the sample standard deviation
n=28 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=28-1=27[/tex]
The Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex],the critical value for this case would be [tex]t_{\alpha/2}=2.052[/tex]
And replacing we got:
[tex]44.7-2.052\frac{6.96}{\sqrt{28}}=42.001[/tex]
[tex]44.7+2.052\frac{6.96}{\sqrt{28}}=47.399[/tex]
And the confidence interval would be between 42.001 and 47.399