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Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply: 83, 12.13) points 53, 11.83) points (8.45, 11.51) points (8.63, 11.33) points Cannot be determined with the information given: Saved

Sagot :

The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .

In the question ,

it is given that ,

90% confidence interval is given as (8.21 , 11.75)

using this interval , we have to find the 95% confidence interval .

Now, [tex]x_{d}[/tex]  - E = 8.21

[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .

Solving the equations ,

we get ,

E = 1.77  and [tex]x_{d}[/tex] = 9.98

So , the margin of error E is given as

E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]

we have to find standard deviation from this ;

given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531

Substituting in the margin of error equation ,

we get ,

S.D. = (1.77 × 4)/1.7531

= 4.0386

So , the 95% confidence interval is given as [tex]x_{d}[/tex]  ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .

from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314

Substituting ,

we get ,

CI = (9.98 ± 2.1314×4.0386/√16)

= (9.98 ± 2.1519)

= ( 9.98 - 2.1519 , 9.98 + 2.1519)

= (7.83 , 12.13)

Therefore , the correct option is (a) (7.83 , 12.13)    .

The given question is incomplete , the complete question is

Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:

(a) (7.83, 12.13)  

(b) (7.53, 11.83)

(c) (8.45, 11.51)

(d) (8.63, 11.33)

Learn more about Confidence Interval here

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