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The sample variance in the strength test values of 15 bricks is 6.89 (MN/m2 ) 2 with a mean of 6.92 MN/m2 . What is the range of the true mean value at the confidence interval of 90%

Sagot :

Cricetus

Answer:

The range of true mean value is "[tex]6.92 \pm 1.11142[/tex]".

Explanation:

The given values are:

Number of bricks,

n = 15

Variance,

σ² = 6.89 MN/m²

Mean,

[tex]\bar{x} = 6.92 \ MN/m^2[/tex]

90% confidence level,

z = 1.64

Now,

The margin of error will be:

= [tex]z\sqrt{\frac{\sigma^2}{n} }[/tex]

On substituting the given values, we get

= [tex]1.64\sqrt{\frac{6.89}{15} }[/tex]

= [tex]1.64\times 0.6777[/tex]

= [tex]1.11142[/tex]

So,

Range of true mean value will be:

=  [tex]Mean \pm Margin \ of \ error[/tex]

=  [tex]6.92 \pm 1.11142[/tex]

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