Autism may be marked by different patterns of brain growth during early life. Researchers measured brain volume (in milliliters, using an MRI) in 26boys who were later diagnosed with autism. Brain volume is also available for 16boys who did not develop autism; these 16boys 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= 26 y₁= 1276.36 s₁= 85.73

Control (group 2) n₂= 16 y₂= 1155.55 s₂= 68.98

1. The null hypothesis for this test is:

H₀: _{1 2}= 0

H₀: _{d1 d2} 0

H₀: _{d1 d2}> 0

H₀: _d= 0

H₀: _d> 0

H₀: _{1 2}> 0

2. The alternative hypothesis for this test is:

H_A: _{d1 d2}> 0

H_A: _{1 2}> 0

H_A: _d 0

H_A: _{d1 d2}= 0

H_A: _d> 0

H_A: _{1 2} 0

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

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

5. The P-value is approximately:

< 0.01

0.01 - 0.05

0.05 - 0.1

0.1 - 0.2

0.2 - 0.5

> 0.5

6. According to the P-value method, what decision would you make?

Because P-value > , I fail to reject H₀.

Because P-value < , I fail to reject H₀.

Because P-value > , I reject H₀.

Because P-value < , I reject H₀.

7. If you incorrectly reject the Null hypothesis, what type of error did you make?

Type-I error

Type-II error

None. If I correctly followed the rejection rule I would not make an error.

8. The 90% confidence interval for the true difference between brain volumes is (give answers to two places after decimal):

lower bound:____upper bound: ____