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Apr 3, 2024

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Name: (Print) Rowan Forsythe____________________________ Section:_____1______ STATISTICS 101 - Module 3a Written Homework According to the US Census Bureau, 37% of US adults between the ages of 25 and 29 have a Bachelor’s degree. 1. Describe the population of interest. The population of interest comes to be US adults between the ages of 25-29 who have a bachelor’s degree. 2. Describe the population proportion of interest in words. What numeric value are we assuming for population proportion here? The population proportion is the amount or percent of the population that fits the interest of the study. For this it would be 37% of people have a bachelor’s degree. 3. What is the sampling distribution for the sample proportion of adults between 25 and 29 years old who have a Bachelor’s degree from a random sample of size 200 from this population? Make sure to explain why the appropriate conditions are met or not met as part of your answer. The sampling distribution for the sampling proportion is normal in this set of data. This would come out to be 200 x 0.37 which would come out to be 74. 4. Suppose in a random sample of 200 adults between 25 and 29 years old, 77 had a Bachelor’s degree. Compute the sample proportion for this sample. P = 77/200 = 0.385 or 38.5 % ^
5. What is the probability that in a sample of 200 adults between 25 and 29 years old, less than 72 of them have a Bachelor’s degree? P (Z < 72 – 74 / 6.824) = P(Z < 0.2931) = 0.6153 6. What is the probability that in a sample of 200 adults between 25 and 29 years old, the sample proportion that have a bachelor’s degree bigger than .41? P (Z > 82 – 74 / 6.824) = P (Z > 1.1723) P (Z > 1.1723) = 1 – P (Z < 1.1723) = 1 – 0.8795 = 0.1205
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