Sample Size and Population

Which conditions hold true based on the central limit theorem? (Check all that apply.)

• If samples of size n = 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n > 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population which is normally distributed, then the sampling distribution of sample means is also normally distributed

Consider a population which is normally distributed. If σ²=9 and n=16, what is the variance of the sampling distribution of sample means? (Do not round off)

Consider a population which is normally distributed. If\sigma=2 and n=9 , what is the standard deviation of the sampling distribution of sample means?

• 0.67

• 0.22

• 0.44

• 1.33

Cellular phone bills for residents of a city have a mean of P1,000 and a standard deviation of P170. Random samples of 100 cellular phone bills are drawn from this population and the mean of each sample is determined. Find the mean of the sampling distribution of sample means.

• 1000

• 170

• 100

• 17

A survey is carried out at Penn State Altoona to estimate the proportion of all undergraduate students living at home during the current term. Of the 3,838 undergraduate students enrolled at the campus, a random sample of 100 was surveyed. What is the population of the study?

• All the 3,838 undergraduate students enrolled at the campus

• The 100 who were surveyed

• All the students in universities across America

• All students living at home in the current term.

What is the entire group studied called?

• sample

• population

• class

• experiment

_______ is the entire group of objects or individuals considered for a survey.

• Sample

• Population

• Random Sample

• Quartile

Population or Sample? A quality control engineer is curious about the thickness of paint on a car at her factory. She randomly selects 30 points on the car and measures the paint thickness at each of those points.

• Population

• Sample

Suppose the training heart rates of all 20-year old athletes are normally distributed, with a mean of 135 beats per minute and standard deviation of 18 beats per minute. Random samples of size 4 are drawn from this population, and the mean of each sample is determined. Find the mean of the sampling distribution of sample means

• 135

• 18

• 4

• 20

Suppose the training heart rates of all 20-year old athletes are normally distributed, with a mean of 135 beats per minute and standard deviation of 18 beats per minute. Random samples of size 4 are drawn from this population, and the mean of each sample is determined. Find the variance of the sampling distribution of sample means