Question

A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength µ greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive strength is 1356 kPa and their standard deviation is 70 kP

Answer 1

Complete question:

new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength µ greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive strength is 1356 kPa and their standard deviation is 70 kP

a) Find the p value.

b) Do you believe it is plausible that the blocks do not meet the specification, or are you convinced that they do? Expain your reasoning.

Answer:

a) p-value= 0.1949

b) It is possible the blocks do not meet the specifications

Explanation:

Given:

n = 100

Sample mean, X' = 1356

Standard deviation, s.d = 70

a) To find p- value.

Null hypothesis:

H0: u ≤ 1350

Alternative hypothesis:

H1 : u > 1350

The test statistic wll be:

$z= \frac{X'-u_o}{s.d/ \sqrt{n}}$

$= \frac{1356-1350}{70/\sqrt{100}}$

=0.86

The p value will be:

= P(z>0.86)

= 1-P(z≤0.86)

Using the normal distribution table, we now have:

1 - 0.8051

= 0.1949

P value = 0.1949

b) Since our p-value is 0.1949, we do not reject the null hypothesis, because the p-value, 0.1949, is not small. This means that it is possible the blocks do not meet the specifications.