Sampling Distributions AP Statistics

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
What is the mean of the sampling distribution of p-hat?

• 0.4

• 0.44

• 0.56

• 0.6

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

• The Population

• The Sample

• The Sampling Distribution

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n is decreased to 25.

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.084

• μ_x-bar = 0.52, σ_x-bar = 0.084

• μ_x-bar = 2.51, σ_x-bar = 0.42

A machine fills bottles of shampoo, the amount poured has a mean of 16 oz and standard deviation 0.5 oz. A sample of 30 shampoo bottles has a mean of 15.8 oz. What is the probability of getting a mean weight of less than 15.8 oz?

• 0.99

• 0.66

• 0.34

• 0.01

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

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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Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg)(kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kgkg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western) ?

Answer explanation

The mean of the sampling distribution of the difference in sample proportions for eastern minus western is equal to the difference in the population proportions, which equals 0.22−0.36

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