Estimating an Average of a Population

Imagine a researcher wants to understand the average time spent on social media by teenagers in a city. What is the purpose of constructing a sampling distribution in this context?

• To estimate the population parameter (average time spent on social media by all teenagers in the city) from the sample statistic (average time from the sample).

• To demonstrate that sample statistics are not useful estimators of population parameters.

• To prove that the sample mean (average time from the sample) is always equal to the population mean (average time by all teenagers in the city).

• To increase the accuracy of the population parameter estimates (average time spent on social media by all teenagers in the city) by using larger samples.

Imagine a study is conducted at a university to determine the average number of textbooks a group of engineering students reads over the course of a semester. Which of the following factors would most likely increase the precision of the sampling distribution of the sample mean?

• Decreasing the sample size

• Increasing the variability of the number of textbooks read

• Increasing the sample size

• Using a convenience sample instead of a random sample

Imagine a researcher is interested in estimating the average height of plants in a large botanical garden. To achieve this, they decide to take samples from different sections of the garden. What is the primary reason for using the sampling distribution of the sample mean in this scenario?

• To directly measure the height of every plant in the garden

• To estimate the average height of plants in the entire garden from the sample means

• To prove that the sampled plants are taller than the rest

• To show that sampling is unnecessary in large populations

Imagine a researcher collecting daily rainfall amounts in a region over a year to calculate the average rainfall. What can be said about the shape of the sampling distribution of these average rainfalls when the sample size is large?

• It is always positively skewed.

• It is always negatively skewed.

• It approaches a normal distribution.

• It becomes a uniform distribution.

If the mean of a sample is 203 and the margin of error is 4.6, what would be a reasonable mean for the population?

• 99.2

• 198.3

• 207.2

• 207.7

• between 5,700 and 6,000

• between 6,500 and 7,000

• between 5,400 and 6,600

• between 5,400 and 5,900

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of the following is closest to the population, in millions, of ninth graders?

• 0.368

• 0.495

• 3.68

• 5.84

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of the following is closest to the population, in millions, of ninth graders?

• 0.368

• 0.495

• 3.68

• 5.84

A random sample of 25 Ohio students had a mean ACT score of 21 with a standard deviation of 1.2.  Which of the following is the 95% confidence interval for the true average ACT score for Ohio students?

• (20.53, 21.47)

• (18.648, 23.352)

• (20.505, 21.495)

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10