Sampling Distribution and CLT

It is a form of probability distribution when all possible samples of size n are drawn repeatedly from the population.

• sampling distribution

• random sampling

• non-random sampling

• probability sampling

In sampling distribution, the mean of the sample means is equal to the ______

• population mean

• population variance

• sample mean

• sample variance

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

A distribution showing the sample means of all sample of size n of a population is called

• Normal Distribution

• Binomial Distribution

• Sampling Distribution

• Uniform Distribution

A car dealership looks back at their previous year’s sales records. Last year, the dealership sold 422 vehicles. The mean sales price was $24,500 with a standard deviation of $12,875. The dealership also discovered that the distribution of the sales prices is skewed to the right. If the dealership were to select repeated random samples of 40 vehicles from the population of all vehicles sold last year and calculate the average sale price for each sample of 40, which of the following gives the correct mean and standard deviation of the sampling distribution of the sample mean?

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A ________ is a probability distribution of a statistic computed from a sample taken from a population.

• Parameter

• Central Limit Theorem

• Confidence Interval

• Sampling distribution.

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

• Group 1

• Group 2

• Group 3

• Group 4

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

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Suppose that it is reported that 42% of the general population regularly recycle. Suppose you decide to take a random sample of Flagler students and ask them if they regularly recycle. You survey 150 students and ask them if they regularly recycle. a) What proportion of your sample would you expect to report that they regularly recycle? ​ (a)   b) What is the standard error for your data? ​ ​ (b)   c) If we increase the sample size from 150 students to 400 students, how will this impact the standard error? ​ (c)  

• 42%

• 0.0403

• decrease

• increase

• 58%

• 0.0343

The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?

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• Cannot be determined because the conditions are not met