Answer:
Step-by-step explanation:
Data given and notation
The info given by the problem is:
the random sample taken
represent the population mean
represent the population standard deviation
The critical region on this case is so then if the value of
we fail to reject the null hypothesis. In other case we reject the null hypothesis
Null and alternative hypotheses to be tested
We need to conduct a hypothesis in order to determine if the true mean is 5000, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Let's define the random variable X ="The compressive strength".
We know from the Central Limit Theorem that the distribution for the sample mean is given by:
Find the probability of committing a type I error when H0 is true.
The definition for type of error I is reject the null hypothesis when actually is true, and is defined as the significance level.
So we can define like this:
And in order to find this probability we can use the Z score given by this formula:
And the value for the probability of error I is givn by: