Question

A random sample of size 11 from a normal distribution has standard deviation s=52. Test H 0 =σ=32 versus H 1 =σ<32. Use the α=0.05 level of significance. Part 1 of 5 The hypotheses are provided above. This hypothesis test is a test. Part: 1/5 Part 2 of 5. Find the critical value. Critical

Answer 1

A student is performing a hypothesis test for a population standard deviation using a sample standard deviation, and is asked to find the critical value. The test uses a chi-squared distribution with degrees of freedom calculated as the sample size minus one.

Step-by-step explanation:

The question asks us to perform a hypothesis test for a population standard deviation using a sample standard deviation (s) of 52 to test the claim that the population standard deviation (σ) is less than 32 (H1: σ < 32) at an α=0.05 level of significance. The null hypothesis in this case would be H0: σ = 32.

To find the critical value, we would use a χ² (chi-squared) distribution, as we are dealing with variances and standard deviations, not the normal distribution. The degrees of freedom (df) would be equal to the sample size minus one: df = n - 1. For a sample of 11, df = 10. Looking up the chi-squared critical value for df=10 at α=0.05 for a left-tailed test gives us the required critical value.