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StatisticsQ&A LibraryYou want to find the average GPA at Adelphi, so you decide to perform a study. You went outside the UC and screamed at people going to lunch, "What's your GPA?" You copied down the first 50 people to answer you. Survey of Statistics Lab Data 1) Discuss the sampling technique(s) used. Do you feel that they could have been improved? Explain. 1.04 2.03 4.14 1.05 2) Display the data in a histogram with the following intervals: 0-1, 1-2, 2-3, 3-4,4-s 0.58 4.02 3.67 2.06 0.67 3) Calculate the mean, median, mode, and range for the study. Also calculate the variance and the sample standard deviation. (Use your calculator.) 3.29 2.23 4) Construct a box and whisker piot of the data. What are the boundaries for the outliers? 3.83 0.24 1.73 5) (a) is it appropriate to use a student's t distribution to compute a confidence interval for the population mean ? 2.53 3.75 2.65 4.98 3.63 (b) Find a 95% confidence interval for " (Show all work and state formulas used.) 4.03 (c) What does the confidence interval mean in the context of this problem? 0.57 2.16 1.06 1.78 0.49 How large of a sample is needed if we wish to be 99% confident that the sample mean is within 25 pts of the population mean score? For this problem, assume that we know that the population standard deviation σ is 1.5. 0.03 4.22 3.21 3.67 1.61 7) Suppose that Adelphi boasts that it has an average GPA of 3.0. Perform a hypothesis test with a level of significance of .05, and anethefHtHeerefeieriemeeef you performed with 50 students is enough to refute this claim. Your final answer must be written in full sentences and reference the math that you performed. (You may assume that the population standard deviation ơ is 1.5.) e4, to see if the study 4.14 0.42 4.31 3.62 4.14 4.09 2.16 1.68 0.99 3.76 0.29 0.85Question

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