Name: [20 points] Written Quiz E [Sections 5.1, 5.2, 6.1-D, 6.1-CI, & 6.1-HT] STA 270: Applied Statistics 1. Suppose we want to test Ha: p = 0.40 vs. HE: p at 0.40 using a sample proportion of 420 out of 1000. You are going to compute the pvalue for this scenario 2 different ways, and then set up a confidence interval for p in this question. a. [1 pt] What is the value of the sample proportion, 15? Give your answer as a decimal. Method 1 The Qvalue from a randomization distribution b. [2 pts] Find the pvalue using a randomization distribution in StatKey [like you would have done in Chapter 4}. PS if you get a randomization distribution that turns all red or shows no red, you may have forgotten to tell StatKey what the null value is. The default null proportion in StatKey is 0.5, but this question is not about a null proportion of 0.50. c. [1 pt] What is the standard error from the randomization distribution in part b? Method 2 The pvalue from a standardized normal distribution d. [2 pts] Verify that the sample proportion for this situation is normally distributed. (Hint: there are two products to compute. Both products must be greater than a certain number. Show that those two products are greater than the appropriate number. These formulas can be found in 6.1D if you are unsure} e. [3 pts] Compute the standard error of the sample proportion using the formula shown in section 6.10. . This number should be close to, but probably not exactly, like the value in 1b above. Show all work