A sample of 54 elderly men take a psychiatric examination to determine whether symptoms of senility are present. A subtest of the Wechsler Adult Intelligence Scale (WAIS) is the explanatory variable. The WAIS scores range from 4 to 20, with a mean of 11.6.

Higher values indicate more effective intellectual functioning.

Software shows the following results:

(a) Show (i) ˆP(y = 1) = 0.50 at x = 7.2, (ii) ˆP(y = 1) <

0.50 for x > 7.2.

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Variable Coef. Std. Error Wald Chi-square Sig.

INTERCEPT 2.0429 1.0717 3.6338 0.0566 WAIS -0.2821 0.1007 7.8487 0.0051

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(b) Estimate the probability of senility at x = 20.

(c) The fit of the linear probability model is ˆP(y = 1) =

0.847 − 0.051x. Estimate the probability of senility at x =

20. Does this make sense?

(d) TestH0: β = 0 againstHa: β = 0.Report and interpret the P-value.