Sampling Distributions Two Sample

Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?

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Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?

• n = 1,000 and p close to 0

• n = 1,000 and p close to 1

• n = 1,000 and p close to 1/2

• n = 100 and p close to 0

• n = 100 and p close to 1/2

The histogram below represents data obtained after the census of an entire population was conducted. The sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution?

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Two random samples, A and B, were selected from the same population to estimate the population mean. For each sample, the mean, standard deviation, and margin of error for a 95 percent confidence interval for the population mean are shown in the table. Which of the following could explain why the margin of error of sample A is greater than the margin of error of sample B?

• The sample size of A is greater than the sample size of B.

• The sample size of A is less than the sample size of B.

• The sample size of A is equal to the sample size of B.

• The mean of sample A is greater than the mean of sample B.

• The standard deviation of sample A is less than the standard deviation of sample B.

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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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

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 kg kg. 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

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

• The Population

• The Sample

• The Sampling Distribution