wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \). \( H_{o}: \mu=53.1 \) \( H_{a}: \mu \neq 53.1 \) believe the population is normally distributed, but you do not know the standard deviation. You obtain ample of size \( n=15 \) with mean \( M=56.5 \) and a standard deviation of \( S D=5.8 \). at is the \( p \)-value for this sample? (Report answer accurate to four decimal places.)

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 \( =\square \)

Question 12 Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1. \( b=\square<b<b)=0.747 \), find \( b \). Submit Question

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.10 \). \[ \begin{array}{l}H_{o}: \mu=51.7 \\ H_{a}: \mu<51.7\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obt: a sample of size \( n=23 \) with mean \( M=45.5 \) and a standard deviation of \( S D=14.1 \). What is the p -value for this sample? (Report answer accurate to four decimal places.) p -value \( =\square \)

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

A population of values has a normal distribution with \( \mu=42.8 \) and \( \sigma=88.4 \). You intend to draw a random sample of size \( n=220 \). Find the probability that a single randomly selected value is less than 36.8 . \( P(x<36.8)= \) Find the probability that a sample of size \( n=220 \) is randomly selected with a mean less that 36.8 . \( P(\bar{x}<36.8)= \) 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.