Stat 101 Module 3a Assignment

Name: Josiah Bartlett Section: 3

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 is US adults between the ages of 25 and 29.

2. Describe the population proportion of interest in words. What numeric value are we assuming for
population proportion here?

The population proportion of interest is 0.37.

This represents the 37% of US adults between the ages of 25 and 29 that 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 conditions that are met would include the following for normal approximation:

1. That the sample is random (meets Randomization Condition).
2. n * p = 74 and n(1-p) = 126, both are greater than 10 (meets Success/Failure Condition).
3. Sample size (n) is less than 10% of the population (meets 10% condition).


We can use normal approximation for this question.

The sample distribution of US adults between the ages of 25 and 29 years old who have a Bachelor’s
degree from a random sample size of 200 would be approximately normal with:

Mean = 200 * 0.37 = 74

Standard Deviation: ((0.37 – 0.63) / 200) ^1/2 = 0.0341

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.

The sample proportion: (77/200) = 0.385

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?

The sample proportion: (72/200) = 0.36

Z-score for the sample proportion: z = (0.36 – 0.37) / (0.0341) = -0.29

Using Z-table, the probability required: (p < 0.36) = (z < -0.29) = 0.3859