Question

A population of 20,000 students at UCSC. 10,400 are Males, 9,200 are Females, and 400 are Other. You take a random sample of n = 100 students. Sample has: 52 Male, 46 Female, 2 Other. In this case, the Chance Error is 0%. *(But it won’t always be 0, in other cases!).

   *(For A, B: SHOW YOUR WORK!)

• A) What is the Population Percentage (e.g., composition)? (HINT: Is it 50%-50%? Something else? Etc.)
• B) What is the Sample Percentage (e.g., composition)?
• C) Is the composition the same for both the Sample and the Population? Yes/No; Explain in a complete sentence.

*For D, E, F: Write out the ENTIRE sentence, and fill-in-the-blank. (Hint: All blanks are numbers).

• D) For the number of Males in the Sample, the Observed Value is ________ and the Expected Value is _________.
• E) For the number of Other in the Sample, the Observed Value is __________ and the Expected Value is _______.
• F) For the number of Females in the Sample, the Observed Value is __________ and the Expected Value is _______.

Answer 1

Answer:

A) The population size of UCSC is 20,000 students. Of them, 9,200 are females and 10,400 are males and 400 are other.

The percentage of each gender in the population is:

Thus, the population percentage is clearly not 50%-50%. Instead, it is Males: Females: Others = 52%-46%-2%.

B) The sample has 100 students. Of these, 52 are males, 46 are females and 2 are others.

Thus, the percentage of each gender in the sample is:

Hence, the sample composition is Males: Females: Others = 52%-46%-2%.

C) As can be seen, the sample and population composition are the same, as they have the same percentage of individuals belonging to each gender.

The expected value is the value that is representative of the population. Since the population and sample composition are the same, the observed and expected values are the same here.

Hence we can write:

D) Observed value for males is 52 and the expected value is also 52.

E) Observed value for others is 2 and the expected value is also 2.

F) Observed value for females is 46 and the expected value is also 46.

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