Sample Distribution

In the general population, 91% of all households own at least one automobile. A sample of 40 people is selected and the sample proportion (p̂) is calculated. Describe the shape of the sample distribution of sample proportions.

• The distribution is skewed to the left.

• The distribution is normally distributed.

• The distribution is skewed to the right.

• The distribution cannot be reasonably created.

• 50

• 25

• 20

• 5

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

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 200

• 16

• 25

• 4

Answer explanation

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

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 200

• 16

• 25

• 4

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

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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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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20 12th graders were asked "How many slides will your presentation have?" Their answers had a mean of 40.35 with an SD of 17.38. If we take a sample of size 4, what is the probability that the average number of slides will be less than 49.04? Enter your answer as a decimal.

Mathematical Equivalence

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