Test Formative - Statistics - Nailesh Soni | Library

Instructions

Distinguish between a parameter and a statistic
Create a sampling distribution using all possible samples from a small population
Using the sampling distribution of a statistic to evaluate a claim about the parameter
Determine if a statistic is an unbiased estimator of a population parameter.
Describe the relationship between sample size and the variability of a statistic.
Calculate the mean and standard deviation the sampling distribution of a sample proportion and interpret the standard deviation.
Determine if the sampling distribution of p-hat is approximately normal.
If appropriate, use a normal distribution to calculate probabilities involving p-hat.

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Quiz Questions

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1

A survey was conducted for Meadowcreek high school students. The mean hours of sleep per night for a random sample (SRS) of 20 students was 6.5 hours. The mean hours of sleep for all the Meadowcreek high school students was 7.5 hours. Which of the following is a correct representation?

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2

Following is a list of four friends and their times spent working out in minutes each day. Alvin 30 Bolt 35 Calvin 25 David 40 List all samples for the sample distributions of sample size 2.

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For the above example list all the samples and the corresponding values of the statistic 'range'.

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A statistic used to estimate a parameter is an unbiased estimator if

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If an SRS is selected, which of the following should be an unbiased estimator of 𝜎?

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2

The mean and standard deviation of the scores on the first semester final for a large statistics class are 349.11 and 61.40 points, respectively. The exam is worth a total of 400 points. To investigate if the sample mean was an unbiased estimator of the population mean, the professor of the class selected 100 SRSs of size 𝑛=10 for all of the students’ scores on the exam. The sample mean for each of these samples was recorded on the dotplot. What would happen to the sampling distribution of the sample mean if the sample size was 𝑛=50 instead?

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The histogram shown shows a sampling distribution intended to estimate the population parameter shown by the arrow. Does the sampling distribution shown illustrate high or low bias? High or low variability?

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In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be most different from 200,000(so for example 300000)?

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A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds. The researchers will report the mean x̄ from their sample as an estimate of the mean cholesterol level 𝜇 in this population. What does it mean to say that x̄ is an unbiased estimator of 𝜇.?

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According to the US Census Bureau the proportion of people living in the metropolitan areas is 80%. Maria selects a random sample of n = 300 people to validate that claim. Let 𝑝̂ = the proportion of people living in the metropolitan area in the sample. Calculate the mean and the standard deviation of the sampling distribution of 𝑝̂ .

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The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Suppose that 30% of all Division I athletes think that these drugs are a problem. Let 𝑝̂ be the sample proportion who say that these drugs are a problem. Is this distribution normal? Write the calculated values and then the interpretation.

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In the United States, 8% of households own a motorcycle. You plan to send surveys to an SRS of 500 households. Let 𝑝̂ be the proportion of households in the sample who own a motorcycle. Describe the shape(normal or not), center (Mean), and variability(Standard Deviation) of the sampling distribution of 𝑝̂ .

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Test Formative - Statistics

Test Formative - Statistics

Name

Email

A survey was conducted for Meadowcreek high school students. The mean hours of sleep per night for a random sample (SRS) of 20 students was 6.5 hours. The mean hours of sleep for all the Meadowcreek high school students was 7.5 hours. Which of the following is a correct representation?

Following is a list of four friends and their times spent working out in minutes each day. Alvin 30 Bolt 35 Calvin 25 David 40 List all samples for the sample distributions of sample size 2.

For the above example list all the samples and the corresponding values of the statistic 'range'.

A statistic used to estimate a parameter is an unbiased estimator if

If an SRS is selected, which of the following should be an unbiased estimator of 𝜎?

The histogram shown shows a sampling distribution intended to estimate the population parameter shown by the arrow. Does the sampling distribution shown illustrate high or low bias? High or low variability?

In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be most different from 200,000(so for example 300000)?

In the above scenario find the probability that greater than equal to 10% of the households own motorcycles?

Name

Email

A survey was conducted for Meadowcreek high school students. The mean hours of sleep per night for a random sample (SRS) of 20 students was 6.5 hours. The mean hours of sleep for all the Meadowcreek high school students was 7.5 hours. Which of the following is a correct representation?

Following is a list of four friends and their times spent working out in minutes each day. Alvin 30 Bolt 35 Calvin 25 David 40 List all samples for the sample distributions of sample size 2.

For the above example list all the samples and the corresponding values of the statistic 'range'.

A statistic used to estimate a parameter is an unbiased estimator if

If an SRS is selected, which of the following should be an unbiased estimator of 𝜎?

The histogram shown shows a sampling distribution intended to estimate the population parameter shown by the arrow. Does the sampling distribution shown illustrate high or low bias? High or low variability?

In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be most different from 200,000(so for example 300000)?

In the above scenario find the probability that greater than equal to 10% of the households own motorcycles?