Question

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%

Answer 1

The range of true mean value is "
`6.92 \pm 1.11142`".

Step-by-step explanation:

The given values are:

Number of bricks,

n = 15

Variance,

σ² = 6.89 MN/m²

Mean,

`\bar{x} = 6.92 \ MN/m^2`

90% confidence level,

z = 1.64

Now,

The margin of error will be:

=
`z\sqrt{(\sigma^2)/(n) }`

On substituting the given values, we get

=
`1.64\sqrt{(6.89)/(15) }`

=
`1.64* 0.6777`

=
`1.11142`

So,

Range of true mean value will be:

=
`Mean \pm Margin \ of \ error`

=
`6.92 \pm 1.11142`