Answer: 0.224 to 0.256
Step-by-step explanation:
As per given , we have
n= 15
df = 14 (df=n-1)
[tex]\overline{x}=0.24\\ s=0.02[/tex]
Significance interval : [tex]\alpha: 1-0.99=0.01[/tex]
Since , population standard deviation is unknown , so we use t-test .
Using t-value table ,
[tex]t_{df,\ \alpha/2}=t_{14,\ 0.005}=2.977[/tex]
99% Confidence interval will be :
[tex]\overline{x}\pm t_{df,\ \alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
[tex]0.24\pm (2.977)\dfrac{0.02}{\sqrt{15}}[/tex]
[tex]\approx0.24\pm 0.015[/tex]
[tex]=(0.24- 0.015,\ 0.24+ 0.015)=(0.225,\ 0.255)[/tex]
Hence, The 99% confidence interval for the average diameter of this electronic component is 0.225 to 0.255.
As we check all the given options , the only closest option is 0.224 to 0.256.
So the correct answer is 0.224 to 0.256.
