Question

In recent years, a substantial amount of research has focused on a possible relationship between chemical contamination of various sorts and mental retardation. An article reported data on hair-lead concentration for a sample of mentally retarded children for which the cause of retardation was unknown. Summary quantities were

   n = 42                 X Bar = 15.56 ppm              s = 6.78 ppm

The paper states that 14.75 ppm is considered the acceptable upper limit of hair-lead concentration.

Let μ= the average hair-lead concentration for all mentally retarded children with the cause of retardation unknown.

H₀: μ = 14.75       versus          H₁: μ > 14.75   at 0.01 significance level

Does the given sample data support the research hypothesis that true average hair concentration for all such mentally retarded chidren exceeds the acceptable upper limit?

		Fail to Reject Null Hypothesis
		Reject Null Hypothesis

Answer 1

H0: = 14.75 ,

Ha: > 14.75  

Test statistics

t = - / S /sqrt(n)

= 15.56 - 14.75 / (6.78 / sqrt(42) )

= 0.774

This is test statistics value.

Critical value at 0.01 level with 41 df = 2.421

Since test statistics < 2.421 , we do not have sufficient evidence to reject H0.

We conclude at 0.01 level that we fail to reject the null hypothesis.