Question

14)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 24 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 overbarequals8.05 cm cubed and sequals0.7 cm cubed. Conduct the appropriate test at the alphaequals0.01 level of significance. State the null and alternative hypotheses. Upper H 0​: mu ▼ less than not equals greater than equals nothing Upper H 1​: mu ▼ greater than equals not equals less than 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. ▼ Fail to reject Reject the null hypothesis. There ▼ is not is sufficient evidence to claim that the mean hippocampal volume is ▼ equal to greater than less than nothing cm cubed. Enter your answer in each of the answer boxes.

Answer 1

Solution :

= 9.02

= 8.05

s= 0.7

n = 24

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 9.02

H_a : < 9.02

Test statistic = t

= ( - ) / s / n

= (8.05 - 9.02) / 0.7 / 12

= -6.79

P(z < - 6.789 ) =-6.79

P-value = 0.000

= 0.01

p = 0 < 0.01, it is concluded that the null hypothesis is rejected.

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is less than 9.02, at the 0.01 significance level