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 27.2 hg < mu < 29.4 hg What is the confidence interval for the population mean mu?

Question
Confidence intervals
asked 2020-11-08
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 \(\mu?\)

Answers (1)

2020-11-09
From the provided information,
Sample size \((n) = 244\)
Sample mean \((\overline{x}) = 28.3 hg\)
Sample standard deviation \((s) = 7.1 hg\)
Since, the population standard deviation is unknown, therefore, the t distribution will be used.
Confidence level \(= 98\%\)
Level of significance \((\alpha) = 1 – 0.98 = 0.02\)
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 \(98\%\) confidence interval can be obtained as:
\(CI = \overline{x} \pm t_{\alpha/2,n-1}\frac{S}{\sqrt{n}}\)
\(= 28.3 \pm (2.34) \frac{7.1}{\sqrt{244}}\)
\(= 28.3 \pm 1.1\)
\(= (27. 2, 29.4)\)
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).
0

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