Question

In a​ study, researchers wanted to measure the effect of alcohol on the hippocampal​ region, the portion of the brain responsible for​ long-term memory​ storage, in adolescents. The researchers randomly selected 20 adolescents with alcohol use disorders 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 overbarequals8.13 cm cubed and sequals0.8 cm cubed. Conduct the appropriate test at the alphaequals0.01 level of significance. State the null and alternative hypotheses. Upper H 0​: mu ▼ equals less than not equals greater than nothing Upper H 1​: mu ▼ greater than equals less than not equals nothing ​(Type integers or decimals. Do not​ round.) Identify the​ t-statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Make a conclusion regarding the hypothesis. ▼ Reject Fail to reject the null hypothesis. There ▼ is not is sufficient evidence to claim that the mean hippocampal volume is ▼ less than equal to greater than nothing cm cubed.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: H:Mean of population Ho 9.02 HA H9.02 Hypothesis test results: Mean Sample Mean Std. Err. P-value DF T-Stat 8.13 0.17888544 19-4.9752512 0.0001

Hence,

Hypotheses:

Ho: $\mu$ = 9.02

H1: $\mu$ < 9.02

t - statistic = -4.98

P - value = 0.000

Reject; is; Less than; 9.02