# Solve and answer this question Are the results between the two confidence intervals very different 27.2 hg < mu < 29.4 hg What is the confidence interval for the population mean mu?

Solve and answer this question Are the results between the two confidence intervals very different
$27.2hg<\mu <29.4hg$
What is the confidence interval for the population mean $\mu ?$
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coffentw
From the provided information,
Sample size $\left(n\right)=244$
Sample mean $\left(\stackrel{―}{x}\right)=28.3hg$
Sample standard deviation $\left(s\right)=7.1hg$
Since, the population standard deviation is unknown, therefore, the t distribution will be used.
Confidence level $=98\mathrm{%}$
Level of significance $\left(\alpha \right)=1–0.98=0.02$
The degree of freedom = n – 1 = 244 – 1 = 243
The critical value of t at 243 degree of freedom with 0.01 level of significance from the t value table is 2.34.
The required $98\mathrm{%}$ confidence interval can be obtained as:
$CI=\stackrel{―}{x}±{t}_{\alpha /2,n-1}\frac{S}{\sqrt{n}}$
$=28.3±\left(2.34\right)\frac{7.1}{\sqrt{244}}$
$=28.3±1.1$
$=\left(27.2,29.4\right)$
Thus, the confidence interval is $27.2<\mu <29.4.$
No, the results between the two confidence intervals are not very different.
The confidence interval limits are almost similar. Therefore, the correct option is B).