Researchers wanted to measure the effector alcohol on the development of the hip

Question

Researchers wanted to measure the effector alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volume in the alcoholic adolescents were less than the normal normal volume of 9.02 cm^3. An analysis of the sample data revealed that the hippocampal volumes is approximately normal with x = 8.17 and s = 0.7. Conduct an appropriate test at the alpha = 0.05 level of significance. Choose the connect hypotheses. Find the test statistic. (Round to two decimal places as needed) Find the P-value. (Round no three decimal places as needed) What conclusion can be drawn?

Explanation / Answer

H0: mu = 9.02
H1: mu < 9.02  

Standard error of the mean, SE = s/sqrt(n) = 0.7/sqrt(12) = 0.202
t = (observed value - hypothesized value)/SE
= (8.17 - 9.02)/0.202 = -4.21
p-value of t=-4.21 and df=n-1= 12-1 = 11 is 0.0007 which is rounded to three decimal place = 0.001
As, p-value < 0.05 (significance level), we reject the null hypothesis and conclude that mu < 9.02

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