Emeli Hagan

2020-11-08

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$\mu ?$

What is the confidence interval for the population mean

coffentw

Skilled2020-11-09Added 103 answers

From the provided information,

Sample size$(n)=244$

Sample mean$(\stackrel{\u2015}{x})=28.3hg$

Sample standard deviation$(s)=7.1hg$

Since, the population standard deviation is unknown, therefore, the t distribution will be used.

Confidence level$=98\mathrm{\%}$

Level of significance$(\alpha )=1\u20130.98=0.02$

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:

$CI=\stackrel{\u2015}{x}\pm {t}_{\alpha /2,n-1}\frac{S}{\sqrt{n}}$

$=28.3\pm (2.34)\frac{7.1}{\sqrt{244}}$

$=28.3\pm 1.1$

$=(27.2,29.4)$

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).

Sample size

Sample mean

Sample standard deviation

Since, the population standard deviation is unknown, therefore, the t distribution will be used.

Confidence level

Level of significance

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

Thus, the confidence interval is

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).

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