Question

Autism may be marked by different patterns of brain growth during early life. Researchers measured brain volume (in milliliters, using an MRI) in 27 boys who were later diagnosed with autism. Brain volume is also available for 15 boys who did not develop autism; these 15 boys serve as the control group. The sample statistics are presented for both groups in the table below. Assume that the population variances are equal. Use a significance level of 0.05 to test for a difference between the autism and control groups.

Groups	Sample size	Sample mean	Sample SD
Autism (group 1)	n1 = 27	y1 = 1296.35	s1 = 86.54
Control (group 2)	n2 = 15	y2 = 1176.13	s2 = 68.32

1. The null hypothesis for this test is:
H₀ : μ₁ − μ₂ > 0
H₀ : μ_d > 0
H₀ : μ_d1 − μ_d2 > 0
H₀ : μ_d = 0
H₀ : μ₁ − μ₂ = 0
H₀ : μ_d1 − μ_d2 ≠ 0

2. The alternative hypothesis for this test is
HA : μ₁ − μ₂ > 0
HA : μ_d > 0
HA : μ_d1 − μ_d2 > 0
HA : μ_d = 0
HA: μ₁ − μ₂ = 0
HA : μ_d1 − μ_d2 ≠ 0

3. The standard error of the estimated difference between the autism and control groups is (give 4 places after decimal)

4. The value of the test statistic is (give 4 places after decimal)

Answer 1