Chapter 7 Quiz--Sampling Distributions

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.

Imagine you are conducting a survey in a large metropolitan area to find out what percentage of residents prefer using public transportation over personal vehicles for their daily commute. If you decide to include more people in your survey, what impact does this have on the sampling distribution of the sample proportion?

• The standard deviation increases.

• The standard deviation decreases.

• The mean of the sampling distribution increases.

• The shape of the distribution becomes more skewed.

Imagine a sports scientist analyzing the sprint times of athletes in a training program to understand performance consistency. They have recorded the sprint times for all participants and wish to calculate the variability of the average sprint time. What formula would they use to calculate the standard deviation of the mean sprint time?

• Sample standard deviation

• Population standard deviation

• Sample mean

• Population mean

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 study is conducted to assess the average daily screen time among college students. Which of the following would most likely result in a biased estimate of the population mean?

• Using a random sample of students from multiple colleges

• Surveying only students from a single study group

• Increasing the sample size

• Ensuring the sample is representative of the entire student population

Imagine a nutritionist conducting a study on the average calorie intake of high school athletes during their training season. What statistical measure would be most appropriate for understanding the spread of average calorie intake across different samples?

• Mode

• Median

• Range

• Standard deviation of the sample mean

Imagine an environmental scientist measuring the pH levels of a lake at different points to assess its acidity. They plan to use these samples to estimate the lake's overall average pH level. Which of the following would most likely result in a more accurate estimation of the population mean?

• Decreasing the number of sampling points

• Sampling only from areas near the shore

• Increasing the number of sampling points

• Sampling only at the lake's deepest points