Answer:
95% Confidence interval: (24.24 ,27.76)
The population mean 28 weeks is not reasonable.
Step-by-step explanation:
We are given the following in the question:
Sample mean = 26
Sample size, n = 50
Alpha, α = 0.05
Sample standard deviation, s = 6.2
95% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 49 and}~\alpha_{0.05} = \pm 2.009[/tex]
[tex]26 \pm 2.009(\displaystyle\frac{2.009}{\sqrt{50}} ) = 26 \pm 1.76 = (24.24 ,27.76)[/tex]
No, it is not reasonable that population mean is 28 weeks because it does not lie in the confidence interval calculated.
