8.3-6. A psychology professor claims that the variance of IQ scores for college students is σ2 = 100. Let X1,X2,...,X23 be a random sample of n = 23 IQ scores and assume these scores come from a N(μ, σ2) distri-bution. Let S2 = (1/22) 23 variance of these scores. (a) Define a critical region for testing H0: σ2 against H1: σ2 = 100. Let α = 0.05. (b) Construct a figure illustrating this critical region. (c) Given that the observed s2 = 147.82, what is your conclusion?
8.3-6. A psychology professor claims that the variance of IQ scores for college students is σ2 = 100. Let X1,X2,...,X23 be a random sample of n = 23 IQ scores and assume these scores come from a N(μ, σ2) distri-bution. Let S2 = (1/22) 23 variance of these scores. (a) Define a critical region for testing H0: σ2 against H1: σ2 = 100. Let α = 0.05. (b) Construct a figure illustrating this critical region. (c) Given that the observed s2 = 147.82, what is your conclusion? (d) Show that Var(S2) = 10,000/11. Thus, the standard deviation of S2 is 30.15. (This helps explain why the critical region you obtained in part (a) is so wide.) (e) Construct a 95% confidence interval for σ2.
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