Final answer:
To evaluate β, we need the p-value and the significance level (usually denoted as α). The given options are not valid for evaluating β
This correct answer is none of the above.
Step-by-step explanation:
In hypothesis testing, β represents the probability of committing a Type II error, which is the probability of not rejecting a null hypothesis when it is actually false.
To evaluate β, we need to know the p-value and the significance level (usually denoted as α).
Given the information provided, we cannot directly evaluate β for the alternatives μ = 4970 and μ = 4960, as we don't have the necessary values.
The given options A, B, C, and D are not valid for evaluating β in this context.
Your correct question is: A new curing process developed for a certain type of cement results in a mean compressive strength of 5000 kilograms per square centimeter with a standard deviation of 120 kilograms. To test the hypothesis that μ=5000 against the alternative that μ<5000, a random sample of 50 pieces of cement is tested. The critical region is defined to be <4970. (a) Find the probability of committing a type I error when H0 is true. (b) Evaluate β for the alternatives μ=4970 and μ=4960.
This correct answer is none of the above.