A researcher wants to find out if U.S. adults still support the death penalty at a proportion of 0.64 (as it was in 2003). This graph indicates the sampling distribution for the proportion of supporters in random samples of 25 adults. The standard deviation is approximately 0.10.What is the approximate test statistic for p̂ = 0.54? −2 −1 0 1 2

7.Suppose the population proportion is 0.200.20 . If the sample size is equal to 5050 , what is the approximate sampling distribution of the sample proportion, P̂ 𝑃^ ?Multiple choice 5 Question 3  N(0.20,0.16)𝑁(0.20,0.16)   N(0.20,0.0032)𝑁(0.20,0.0032)   N(0.20,0.057)𝑁(0.20,0.057)   N(0.80,0.16)𝑁(0.80,0.16)

A Gallup Poll in May 2004 estimated that roughly 70% of U.S. adults are in favor of the death penalty for a person convicted of murder. A random sample of 750 U.S. adults is chosen. Let X be the number of adults (out of 750) who favor the death penalty.The distribution of X is binomial. What are the values of n and p?

What is the sampling distribution of the sample proportion (p-hat)? In other words, what can we say about the behavior of the different possible values of the sample proportion that we can get when we take such a sample? (Note: normal approximation is valid because .1(225) = 22.5 and .9(225) = 202.5 are both more than 10.)Reset this ActivitySince the sample proportion has a normal distribution, its values follow the Standard Deviation Rule. What interval is almost certain (probability .997) to contain the sample proportion of left-handed people?Reset this ActivityIn a sample of 225 people, would it be unusual to find that 40 people in the sample are left-handed?Reset this ActivityFind the approximate probability of at least 27 in 225 (proportion .12) being left-handed. In other words, what is P(p-hat ≥ 0.12)?Guidance: Note that 0.12 is exactly 1 standard deviation (0.02) above the mean (0.1). Now use the Standard Deviation Rule.

Withdrawal symptoms may occur when a person using a painkiller suddenly stops using it. For a special type of painkiller, withdrawal symptoms occur in 4% of the cases.A random sample of 2400 people who have stopped using the painkiller is going to be taken. Let p be the proportion of people in the sample who experience withdrawal symptoms.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P>p0.05, which is the probability that more than 5% of the people in the sample experience withdrawal symptoms. Round your answer to four decimal places.

According to previous studies, 16% of the U.S. population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the U.S. is 15%.The student is going to take a random sample of 2100 people in the U.S. to try to gather evidence to support the claim. Let p be the proportion of left-handed people in the sample.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P≥p0.15, which is the probability that there will be 15% or more left-handed people in the sample. Round your answer to four decimal places.