Question

Scores on an IQ test are normally distributed. A sample of 25 IQ scores had standard deviation of 8. The developer of the test claims that the population standard deviation of 15. Do these data provide sufficient evidence to significance? Use =0.05α=0.05 . Test by using a confidence interval. Show step1-step3.

Answer 1

Yes, the data provides sufficient evidence at 0.05 level of significance

Explanation:

n = 25

s = 8

σ = 15

χ² = (n - 1)s² / σ²

χ² = (25 - 1)*8² / 15²

χ² = (24 * 64) / 225

χ² = 6.827

The critical value at 0.05 ; df = 25 - 1 = 24

12.4012 and 39.3641

Reject H0 if χ² < 12.4012 or if χ² > 39.3641

Since,

χ² < 12.4012 ; We reject H0 ;