Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 7.9 9.7 9.7 8.7 7.0 7.2 11.3 11.8 7.3 8.1 8.0 11.6 6.8 9.0 6.3 7.0 7.4 8.7 6.8 5.8 7.8 7.7 6.3 7.0 7.7 6.5 10.7 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 219.8.] (Round your answer to three decimal places.) MPa

Answer 1

`\sum X_i = 219.8`

And we can calculate the mean with the following formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)= (219.8)/(27)= 8.141`

We can calculate the sample variance with this formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)= 2.819`

And the sample deviation would be given by:

`s= √(s^2)=√(2.819)= 1.679`

Explanation:

For this case we have the following data given:

7.9 9.7 9.7 8.7 7.0 7.2 11.3 11.8 7.3 8.1 8.0 11.6 6.8 9.0 6.3 7.0 7.4 8.7 6.8 5.8 7.8 7.7 6.3 7.0 7.7 6.5 10.7

Our variable of interest is given by X="flexural strength (MPa) for concrete beams of a certain type"

And for this case we know that
`\sum X_i = 219.8`

And we can calculate the mean with the following formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)= (219.8)/(27)= 8.141`

We can calculate the sample variance with this formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)= 2.819`

And the sample deviation would be given by:

`s= √(s^2)=√(2.819)= 1.679`