The following is a lab report students were asked to complete in conjunction with the following on-line lab assignment. Page 7 of the lab is where students begin to focus on inference.http://statweb.calpoly.edu/bchance/stat217/labs/lab8/lab8_1.htmlStat 217 - Lab 8 ReportData Collection(a) Write a paragraph summarizing the key characteristics of this study. In particular, identify:- observational units (and sample size) - population of interest- response variable and whether its quantitative or categorical- explanatory variable and whether its quantitative or categorical- type of study (observational of experimental) and why- the types of randomness used in the study (random assignment or random sampling or both or neither) Descriptive Statistics (b) Include your graphical summary of the data here.Is the direction of the association as expected by the student researchers (clarify what was expected)? Would you consider it a strong association? (In other words, does knowing a person’s study hours help you accurately predict their GPA?)(c) Include your correlation coefficient output here.Does the correlation coefficient indicate a positive or a negative linear association here? Does it seem strong or weak?(d) Include your regression equation output here, including scatterplot with line superimposedProvide a detailed (statistical) interpretation of both the intercept and the slope coefficients.Statistical Inference(e) Did you get the same sample regression line?(f) Describe the behavior of the sample regression lines as they scroll by. That is, describe howthey change from sample to sample.(g) Insert Slope Dot Plot hereDescribe the distribution of the slope coefficients. Hint: Remember to discuss shape, center, and spread of this sampling distribution. Be sure to report the mean and standard derivation of these values (as reported in the upper left corner of the "Slope Dot Plot"). Does the value of the mean (approximately zero) make sense? Explain.(h) How does the student project group’s line compare to the regression lines you simulated (believing - = 0)? Roughly how many of the 500 simulated sample slopes are as large or larger than the slope coefficient from the student project (0.0894)? What does this suggest about the size of the p-value for testing whether the population slope is zero against the alternative hypothesis that it is positive? What conclusion would you draw about those hypotheses? Explain.(i) Using the standard deviation you found in (g), how many standard deviations is the observed sample slope (0.0894) from the hypothesized slope (0.0)? Show your work.Extra Credit: Change the sample size from 80 to 40 and generate 500 random samples. Describe the changes in the sampling distribution of the slope and the empirical p-value. (Include a screen capture of both dotplots.) Do they change in the expected manner? Explain.(j) Include Stat > Regression > Regression output here (the 2 lines giving the regression equation, and the 3 lines starting Predictor, Constant, and Study Hours)(k) How does the SE Coef value corresponding to the study hours row compare to the standard deviation of the slopes found in (g)? How does this t-value compare to what you found in (i)? How does the p-value compare to the one-sided p-value you estimated in (h)? (l) Write a few sentences summarizing your analysis, in particular, for this research study:- What did you learn from the scatterplot and the correlation coefficient about the sample data? - What did you learn from the test statistic and p-value?- What are your final conclusions about the relationship between study hours and GPA forthis population and how do they follow from these analyses? - What population are you willing to generalize these results to? Are you able to draw a cause-and-effect conclusion between studying and GPA? Explain. - What concerns do you have about how these data were collected and how that might impact the conclusions you can draw form this study? Keep in mind, there is a difference between the strength of the relationship and the strength of evidence against the null
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