Problem 1 In 2012, 71% of student graduating from a four-year college had student loan debt. 1. We randomly sample colle

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Problem 1 In 2012 71 Of Student Graduating From A Four Year College Had Student Loan Debt 1 We Randomly Sample Colle 1 (73.83 KiB) Viewed 13 times

Problem 1 In 2012 71 Of Student Graduating From A Four Year College Had Student Loan Debt 1 We Randomly Sample Colle 2 (73.83 KiB) Viewed 13 times

Problem 1 In 2012 71 Of Student Graduating From A Four Year College Had Student Loan Debt 1 We Randomly Sample Colle 3 (65.51 KiB) Viewed 13 times

Problem 1 In 2012, 71% of student graduating from a four-year college had student loan debt. 1. We randomly sample college graduates from four-year universities an determined the proportion in the sample with student loans. For which of the following sample sizes is a normal model a good fit for the sampling distribution of sample proportions? A sample size of 40 ✔ is/are appropriate. (Click to view hint) 2. If we randomly sample 50 students at a time, what will be the mean and the standard deviation of the distribution of sample proportions? x (Enter as a decimal.) (Click to view hint) x (Round to the nearest thousandth.) (Click to view hint) H₂=2 %₂ = 50 Problem 2 According to the official M&Ms website, 24% of the plain milk chocolate M&Ms produced by Mars Corporation are blue. Annie buys a large family-size bag of M&Ms. Sarah buys a small fun-size bag. Which bag is more likely to have more than 40% blue M&Ms? Sarah, because there is more variability in the proportion of blues among smaller samples.✔ (Click to view hint) Problem 3 Imagine you have a very large barrel that contains tens of thousands of M&Ms. According to the official website, 20% of the M&Ms produced by the Mars Corporation are orange. Five students each take a random sample of 50 M&Ms and record the percentage of orange in each sample. Which sequence is the most nlausible for the percentage of orange candies obtained in these 5 samples? Sa Sar Sim Norn Distri 15 16 Lesso Finish atter
s out of g tion If a sampling distribution is normally shaped, we can apply the Empirical Rule and use z-scores to determine probabilities. Let's look at some examples. Example A random sample of 100 students is taken from the population of all part-time students in the U.S., for which the overall population of females is 0.6. Start by determining what is given in the original statement. 100 0.6= Test to see if we can use the normal distribution. np= and ng= Can we use the normal approximation? Since the population proportion is p=0.6, we know the mean of the sampling proportions is = (Hint: H, = p.) What is the standard deviation? o Probability 1 There is a 95% chance that the sample proportion, p, falls between what two values? We are looking for two x- values between which 95% of the data lies. By the Empirical Rule, we know that 95% of the data in a normal distribution falls between 2 standard deviations. Therefore we need to find the z-values (the raw data scores) for ₁ = H-20 and ₂ H₂ +20, #1=0.6-2(0.049) 0.502 = 06 210.049)-0.608 Ta (Round to the nearest thousandth.) Hint: o H 29 Le Fini