Which of the following is NOT a requirement of terting a claim about two population means when \( \sigma_{1} \) and \( \sigma_{2} \) are unknown and not assumed to be equal? Choose the correct answer below. A. The two samples are independent. B. The two samples are dependent. C. Either the two sample sizes are large \( \left(n_{1}>30\right. \) and \( \left.n_{2}>30\right) \) or both samples come from populations having normal distributions, or both of these conditions are satisfied. D. Both samples are simple random samples.

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.

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.

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

Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.7944 \), find \( b \). \( b=\square \) 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 \( =\square \)