Learning Activity 1.1

If a full population survey costs $50,000 and takes 6 months, but a sample survey of 10% of the population costs $10,000 and takes 1 month, what is the cost saving of the sample survey?

• $30,000

• $35,000

• $40,000

• $45,000

If a cluster sampling method is used and a population is divided into 50 clusters of 20 individuals each, how many clusters should be randomly selected to get a sample of 200 individuals?

• 5

• 10

• 15

• 20

If the probability of selecting an individual in a simple random sample of size 50 from a population of 500 is to be calculated, what is that probability?

• 0.01

• 0.05

• 0.10

• 0.50

A researcher wants to estimate the average height of students in a university. If the university has 10,000 students and the sample mean height from 200 students is 170 cm, what is the estimated total height of all students?

• 1,700,000 cm

• 1,750,000 cm

• 1,800,000 cm

• 1,850,000 cm

Answer explanation

Explanation: 170 cm × 10,000 students = 1,700,000 cm

What is the time saved if a full census survey takes 8 months and a sample survey of 15% of the population takes 2 months?

• 4 months

• 5 months

• 6 months

• 7 months

Answer explanation

Explanation: 8 months - 2 months = 6 months

For a population with a mean of 100 and a standard deviation of 20, a simple random sample of 25 is taken. What is the standard error of the sample mean?

• 4

• 5

• 6

• 7

In a stratified sampling method, a researcher divides a population into 4 strata with sizes 100, 200, 300, and 400. If the researcher wants to take a sample of 100 individuals proportional to the strata sizes, how many individuals should be sampled from the largest stratum?

• 20

• 30

• 40

• 50

If a sample survey is conducted to estimate the proportion of a population that prefers a new product, and 120 out of 400 sampled individuals prefer the product, what is the estimated proportion?

• 0.20

• 0.25

• 0.30

• 0.40

In conducting a sample survey, a researcher decides to use a confidence level of 95% for estimating the population mean. If the z-score for 95% confidence is 1.96 and the sample standard deviation is 10 with a sample size of 36, what is the margin of error?

• 2.67

• 3.27

• 3.93

• 4.12

If a population has a standard deviation (σ) of 15, what is the standard error (SE) of the mean for a simple random sample of 100?

• 1.5

• 1.8

• 2.0

• 2.5