Researchers wanted to measure the effect of alcohol on the development of the hi

Question

Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 11 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm cubed. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbar equals 8.26 and sequals0.7. Conduct an appropriate test at the alphaequals0.05 level of significance. Choose the correct hypotheses. Upper H 0?: ? sigma mu p ? not equals less than greater than equals 9.02 Upper H 1?: ? sigma p mu ? not equals equals greater than less than 9.02 Find the test statistic. t 0equals nothing ?(Round to two decimal places as? needed.) Find the? P-value. The? P-value is nothing. ?(Round to three decimal places as? needed.) What conclusion can be? drawn? A. Do not reject Upper H 0. There is not nbspsufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are greater than the normal volume of 9.02 cm cubed. B. Reject Upper H 0. There is not nbspsufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm cubed. C. Do not reject Upper H 0. There is nothingsufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are greater than the normal volume of 9.02 cm cubed. D. Reject Upper H 0. There is nothingsufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm cubed.

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H0 : ? = 9.02
HA : ? < 9.02

Hypothesis test results:

Hence,

Ho: ? = 9.02

Ha: ? < 9.02

Test statistic = -3.60

p - Value = 0.002

Conclusion: Option D is correct.

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