Question

For a simple random sample of adults, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A simple random sample of 13 statistics professors yields a standard deviation of s = 7.2. Assume that IQ scores of statistics professors are normally distributed and use a 0.05 significance level to test the claim that  = 15. Use the Traditional Method

Answer 1

Null and alternative hypotheses

Ho : = 15

Ha : 15

Level of significance a = 0.05

Test statistic

2 = ( n-1)*s​​​​​​2/ 2

= 12* 7.22/152

  2 = 2.76

  2critical value for a = 0.05 , d.f = n -1 = 12

Using chi square table

  2critical = 20.025, 12

2critical = 4.40 , 23.34

Decision rule : if chi square < 4.40 or > 23.34 we reject the null hypothesis otherwise fail to reject the null hypothesis

Here 2.76 < 4.40

Decision : we reject the null hypothesis

Conclusion : There is no sufficient evidence to support the claim that = 15