The average IQ of 48-month old girls is 108. A random sample of 36 adopted girls

Question

The average IQ of 48-month old girls is 108. A random sample of 36 adopted girls was found to have a mean IQ of 103 with a standard deviation of 18. Is it reasonable to conclude that the mean IQ of adopted girls is different from that of the general population of 48-month old girls? Please answer the question by providing (a) two hypotheses along with assumptions, (b) significance level (use 0.05 level), (c) critical values with appropriate df, (d) decision rules, (e) computations, and (f) decision and interpretation

Explanation / Answer

Question a)

Null Hypothesis (H0): µ = 108

Alternative Hypothesis (H1): µ ¹ 108

Assumptions:

The distribution of the parent distribution is approximately normal.

The samples are selected randomly and independently.

Question b)

The level of significance is .05

Question c)

From normal table we get the critical values as -1.96 and +1.96.

Question d)

The null hypothesis can be rejected if | z | 1.96

Question e)

z = (x bar - µ) / (s / Ön)

   = (103 – 108)/(18/sqrt(36))

   = -1.67

| z | = 1.67

Question f)

| 1.67 | < 1.96; we fail to reject the null hypothesis.

At 5% level of significance there is not sufficient evidence to conclude that the mean IQ of adopted girl is different from that of the general population of 48-month old girls.

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