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Unformatted text preview: Try It! Completing a Graduate Degree A researcher has taken a random sample of n = 100 recent college graduates and recorded whether or not the student completed their degree in 5 years or less. Based on these data, a 95% confidence interval for the population proportion of all college students that complete their degree in 5 years or less is computed to be (0.62, 0.80). a. How many of the 100 sampled college graduates completed their degree in 5 years or less? The sample proportion is the midpoint of 0.71, so 71% of 100 is 71. b. Which of the following statements gives a valid interpretation of this 95% confidence level? Circle all that are valid. i. There is about a 95% chance that the population proportion of students who have completed their degree in 5 years or less is between 0.62 and 0.80. ii. If the sampling procedure were repeated many times, then approximately 95% of the resulting confidence intervals would contain the population proportion of students who have completed their degree in 5 years or less. iii. The probability that the population proportion p falls between 0.62 and 0.80 is 0.95 for repeated samples of the same size from the same population. Look up 0.025 or 0.975 in the middle of Table A.1 and the (closest) z value is 1.96 What about that Multiplier of 2? The exact multiplier of the standard error for a 95% confidence level would be 1.96, which was rounded to the 95% value of 2. Where does the 1.96 come from? Use the standard normal distribution, the N(0, 1) distribution at the 0.025
right and Table A.1. Look up 0.05 Researchers may not always want to use a 95% confidence and closest level. Other common levels are 90%, 98% and 99%. z = ‐1.645; look up 0.95 90% get z = 1.645 Using the same idea for confirming the value of 1.96, find the 0.05
correct multiplier if the confidence level were 90%. The generic expression for this multiplier when you are working with a standard normal distribution is given by z*. The table on the next page provides some of the multipliers for a population proportion confidence interval (page 412 of your text). 78 ...
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- Winter '10