Question

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

Answer 1

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 100 kilograms. To test the hypothesis that µ = 5000 against the alternative that µ < 5000, a random sample of 25 pieces of cement is tested. The critical region is defined to be x<4970. Find the probability of committing a type I error when H0 is true.

Answer 2

Find the probability of committing a type I error:

Explanation:

• We have,  n = 50,
• μ = 5000,
• σ =120
• If x bar falls in the interval x bar ≥ 4970, we accept
• the null hypothesis H_0 : μ = 5000;
• Otherwise, we accept
• the null hypothesis H1 : μ ≠ 5000