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.

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.

We collect random samples of 25 students at a time and calculate the proportion of females in each sample. The standard deviation of p-hats is approximately 0.10. Which of the following is a plausible standard deviation for samples of 100?

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

The sampling distribution of the sample proportion is the distribution of values of the sample proportion from all possible samples of size n drawn from a population. When a sample proportion is calculated, the population from which the sample comes is discrete. The variance of the sample proportion is equal to the variance of a binomial random variable divided by the sample size squared. The sampling distribution of the sample proportion is approximately normally distributed provided the population is normally distributed.

Let’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?