Question

A construction company is making a huge batch of thousands of concrete blocks for a new project. The mean weight among all the blocks should be 25 kg. It is too time consuming to conduct a census and weigh every single block, so the company randomly selects 15 blocks to weigh. The sample mean weight among the 15 blocks is 25.5 kg and the sample standard deviation is s = 0.6 kg. σ is unknown. Assume the population of weights is normally distributed. Do you have significant evidence that μ is different from 25 kg? Report ?0, ??, the rejection region (use α = .10), test statistic, conclusion, and place bounds on the p-value.

Answer 1

To Test :-

H0 :- µ = 25
H1 :- µ ≠ 25

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 25.5 - 25 ) / ( 0.6 / √(15) )
t = 3.2275

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.1 /2, 15-1) = 1.761
| t | > t(α/2, n-1) = 3.2275 > 1.761
Result :- Reject null hypothesis

Conclusion :- There is sufficient evidnece to support the claim that  μ is different from 25 kg.

P - value = P ( t > 3.2275 ) = 0.0061 ( From t table )