Researchers selected 872 patients at random among those who take a certain widely-used prescription drug daily. In a clinical trial, 27 out of the 872 patients complained of flulike symptoms. Suppose that it is known that \( 2.7 \% \) of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than \( 2.7 \% \) of this drug's users experience flulike symptoms as a side effect at the \( \alpha=0.1 \) level of significance? Because \( n p_{0}\left(1-p_{0}\right)=\square \) selected at random, all of the requirements for testing the hypothesis \( \square \) satisfied. (Round to one decimal place as needed.)

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 \( =\square \)

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

CNNBC recently reported that the mean annual cost of auto insurance is 1047 dollars. Assur the standard deviation is 291 dollars. You take a simple random sample of 64 auto insurance policies. Find the probability that a single randomly selected value is less than 991 dollars. \( P(x<991)= \) Find the probability that a sample of size \( n=64 \) is randomly selected with a mean less tha 991 dollars. \( P(\bar{x}<991)= \)