Question 8

1 PointNow we’ll explore the sampling distribution for a mean by looking at health care expenditures for each country (as a percentage of all government expenditures). Click on the RED StatKey box in upper left corner of your Statkey screen.Then select sampling distribution for a mean. Click on UPLOAD FILE and choose the All Countries.csv file that you downloaded at the beginning of this activity. Select the column labeled HEALTH.Note: This data includes some missing values, so is not really data on the entire population of all countries, but it is close, and for the purposes of this lab we’ll pretend it represents data on the entire population of all countries.

After viewing the All countries.csv data in StatKey, fill in the following information about the POPULATION:The number of countries (with health care expenditures) in this population is : Blank 1The mean health care expenditure in this population is Blank 2 (enter value as shown in statkey)The population has a distribution shape that is Blank 3

(For shape type only one or two words, i.e. symmetric, right skewed, left skewed)

Blank 1

Blank 2

Blank 3

Question 9

2 PointsThe default sample size is n = 10, and we can keep this. Now the process is the same as before –1) click Generate 1 Sample to draw a random sample of 10 countries from the population. Like before, the sample data will be displayed under Sample and the sample statistic (now the mean) will be plotted with a dot on the sampling distribution.2) Click on “Show Data Table” next to Sample to see which countries you randomly selected to be in your sample.THINK: What is the sample mean of your sample? How do the summary statistics (mean, median, standard deviation) of the random sample compare to the parameters in the population?3) Repeat step (2) several times. Try to get a feel for the following: How much do sample means tend to be varying from sample to sample? h. How do the sample statistics (random) relate to the population parameters (fixed)?

4) Generate 1000 samples to get a sampling distribution for the mean.

THINK: What is the mean of the sampling distribution? Why? What is the standard error of the sample mean? Describe the shape of the distribution. What is the farthest value from the truth?Try hovering your mouse over any of the dots to see the sample it came from. Remember – each dot is a statistic from a sample!

Submit a screenshot of your final sampling distribution(after generating at least 1000 samples)

Question 10

1 Point

Which of the following best describe the shape and the mean of your sampling distribution in the screenshot above?

the distribution is approximately symmetric with a mean much larger than the population mean

the distribution is right-skewed with a mean much larger than the population mean

the distribution is left-skewed with a mean much less than the population mean

the distribution is approximately symmetric with a mean about equal to the population mean

Question 11

1 Point

How does the standard deviation of the statistic (the standard error of the mean) compare to the standard deviation of the actual population?

Note: In the right panels each dot corresponds to a single country, while in the sampling distribution each dot is the mean for 10 countries. Although both distributions have a standard deviation, they are measuring standard deviation of two very different distributions/quantities.

The standard error is the same as the standard deviation of the actual data

The standard error is larger than the standard deviation of the actual data

The standard error is smaller than the standard deviation of the actual data

Question 12

0.5 PointsHit the Generate 1 Sample button one more time and note the sample mean of this sample (lower right corner graph).What was this sample’s mean?

Integer, decimal, or E notation allowed

Question 13

0.5 PointsWhat is the standard error of your sampling distribution of the sample mean (large graph) from your screenshot submitted in Question 9 above?

Integer, decimal, or E notation allowed

Question 14

1 Point

Use the mean and standard error values in Questions 12 & 13 to compute an upper and a lower bound for estimating the population mean as follows:

Lower bound: Mean – 2 *Standard_error Upper bound: Mean + 2 * Standard_error

Does the population mean (from Question 8) lie within these bounds?

Yes

No

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