1.)Suppose that a recent poll found that in a random sample of 2,692 registered voters, 69% supported an increase in the minimum wage.

a)A test of significance for a proportion, also called a 1-proportion z-test will allow us to determine if voters who are registered as independent will have a lower proportion than the overall group. Identify the unknown parameter.

b)State the null and alternative hypotheses.

c)Assume that the 69% observed in the poll is in fact the proportion of all registered voters who favor raising the minimum wage. Suppose we plan on taking a random sample of 898 independent voters. We need to check all the conditions. What can be assumed about the sampling distribution of the sample proportion who favor raising the minimum wage for those who are registered independents?

d)Suppose form the sample of 898 voters who are registered as independents, a random sample produced 594 favoring a raise in the minimum wage. What is the proportion of independent voters in favor of raising the minimum wage in your sample? What is the z-score associated with that proportion?

e)What is the probability that you observe a proportion who favor an increase in the minimum wage smaller than would actually be observed in the overall population of voters? In other words, what is the probability to the left of your z-score?

f)State a conclusion in the context of the problem for a 5% level of significance.

g)Describe what a Type I and a Type II error would represent in this context.

1.)Based on the Preview Assignment, explain what happens to the formula if we keep one unknown constant and increase the other.

a)If is held constant and n is increased.

b)If n is held constant and is increased.

2.)Suppose we have the population 1, 2, 3, 3, 5.

a)What is the population mean and standard deviation?

b)How many different samples of size n = 2 (with replacement) can be constructed? Consider that there are 5 options to choose from.

c)What should the values of the mean and standard deviation of the sampling distribution be?

3.)Suppose there are 100 individuals and you want to have samples of size 36 (to guarantee that the dot plot can be approximated by a normal curve). Suppose also that the population standard deviation is 0.9 and the population mean is 12. If you randomly select a sample of 36 individuals and the sample mean is 12.65. What is the z-score for this situation? Would you consider this case to be common or rare?