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 \( 9.02 \mathrm{~cm}^{3} \). An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \( \bar{x}=8.14 \mathrm{~cm}^{3} \) and \( \mathrm{s}=0.7 \mathrm{~cm}^{3} \). Conduct the appropriate test at the \( \alpha=0.01 \) level of significance. Identify the P-value. P-value \( =0.000 \) (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. \( \square \mathrm{cm}^{3} \).

pulation of values has a normal distribution with \( \mu=54.8 \) and \( \sigma=41.4 \). You intend to draw a dom sample of size \( n=206 \). \( >52.2)=\square \) the probability that a single randomly selected value is greater than 52.2 . \( > \) the probability that a sample of size \( n=206 \) is randomly selected with a mean greater than 52.2 . \( >52.2)=\square \) er your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \)-scores or \( z \) - res rounded to 3 decimal places are accepted.

A population of values has a normal distribution with \( \mu=116.7 \) and \( \sigma=12.4 \). You intend to draw a random sample of size \( n=151 \). Find the probability that a single randomly selected value is less than 115.5 . \( P(x<115.5)= \) Find the probability that a sample of size \( n=151 \) is randomly selected with a mean less than 115.5 . \( P(\bar{x}<115.5)= \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \)-scores or scores rounded to 3 decimal places are accepted. Submit Question

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.05 \) \[ \begin{array}{l}H_{o}: \mu=72.3 \\ H_{a}: \mu \neq 72.3\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obta a sample of size \( n=5 \) with mean \( M=78.2 \) and a standard deviation of \( S D=18.8 \). What is the p-value for this sample? (Report answer accurate to four decimal places.) -value \( =\square \)

Score on last try: 0 of 1 pts. See Details for more. \( > \) Next question Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.6956 \), find \( b \). Submit Question

population of values has a normal distribution with \( \mu=247.9 \) and \( \sigma=53.8 \). You intend raw a random sample of size \( n=54 \). ind the probability that a single randomly selected value is greater than 269.9 . Find the probability that a sample of size \( n=54 \) is randomly selected with a mean greater than 269.9 . \( P(\bar{x}>269.9)=\square \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \) scores or \( z \)-scores rounded to 3 decimal places are accepted.