The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? \( \begin{array}{l}\mathrm{H}_{0}: \sigma=4.2 \\ \mathrm{H}_{1}: \sigma \neq 4.2 \\ \text { Two-tailed } \\ \text { Left-tailed } \\ \text { Right-tailed }\end{array} \) ?

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.

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.

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 \( =\square \)

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

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