The Naive Comparison - Sampling and Statistical Inference - Population Correlation Coefficient - Statistics Assignment Help

Assignment Task:

1. Suppose you are studying the research question whether having a COVID decreases students’ academic performance. 

a) What is the naïve comparison? Why can it be misleading? 

b) What is the ideal comparison? Is it ever feasible to make the ideal comparison? 

2. Explain the following concepts: parameter, statistic, sampling and statistical inference. Give an example of a parameter and statistic.

6. What is a population distribution and what is a sampling distribution? Give an example for each distribution. Explain the major differences. Which one are we using when performing statistical inference? 

7. The attention span of a two-year-old is normally distributed with a mean and standard deviation both about 10 minutes. Suppose we randomly survey 60 two-year-olds. Which do you think is higher? Explain. 

• The probability that an individual baby’s attention span is less than 20 minutes 

• The probability that the average attention span for the 60 children is less than 20 minutes 

8. Explain what central limit theorem is and why it is important in statistical inference 

9. Suppose a new standardized test is given to 50 randomly selected third-grade students in New Jersey. The sample average score X on the test is 62 points, and the sample standard deviation, s, is 8 points. 

a. The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders.

b. Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 65 points and sample standard deviation of 11 points. Construct a 90% confidence interval for the mean score of all Iowa third graders.

STATA HINTS: First load STATA and type “edit,” which brings up something that looks like a spreadsheet. Enter the smoking and cancer values in the first two columns. Double- click the column headers to enter variable names (e.g. “smoke”, “death”). Close the editor window when you are done. The following commands will be useful: 

list: lists the data (to be sure you typed it in correctly) 

summarize: computes sample means and standard deviations (the option “,detail” gives additional statistics, including the sample variance) 

correlate: produces correlation coefficient (with the option “,covariance” this command produces covariances)

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