Question 1 From Bahcesehir university, independent random samples of 25 female students and 20 male students from the Faculty of Economics and Administrative Sciences. There is no historical information about either the population standard deviation of GPAs for female students or male students but they are assumed to be equal. Using the "gpa.csv" dataset, a) Compute the 95% confidence interval for the difference between the population mean GPAs of female and male students and interpret your result. (Manual Solution). b) Compute the 95% confidence interval for the difference between the population mean GPAs of female and male students (Manual Computation using R). Rc) Using the relevant predefined function, validate your answer in parts a and b. Question 2 A study investigated the recovery period for COVID-19 patients in two different countries namely Country 1 and Country 2. Researchers tested the claim that average recovery period (in days) in Country 1 is longer than Country 2 at 1% significance level using random samples of 10000 patients in Country 1 and 7500 patients in county 2 who have recovered. a) Conduct the hypothesis testing procedure using critical value approach and interpret your result (Manual Solution). b) Validate your result in part a) manually using R. (Use p-value approach). (Manual Computation) c) Using the relevant predefined functions, validate your answer in parts a and b by applying both critical value and p-value approaches. Question 3 A researcher studies wage discrepancies among the seven regions of the Turkey and considers the full-time, hourly-wage workers between the ages of 20 and 40. Researchers randomly selected 200 workers meeting the age criteria from Marmara Region, Aegean Region, Mediterranean Region, Black Sea, Central, Anatolian, Eastern Anatolian and Southern Anatolian Region recorded their hourly pay rates. According to the proper analysis what conclusions can the researchers make at 97.5% confidence level? a) Set your null and alternative hypothesis then conduct the analysis manually using p-value approach and interpret your result (Manual Computation using R). b) Validate your result in part a) using the proper predefined function R (Use critical-value approach). c) Using the "aov" function construct the anova table using R. File Home Insert Formulas Data Review View Help Tell me what you want to do X Cut v Paste Copy BIUD ab $ % 950898 Format Painter Undo Clipboard Font Alignment Number C1 fx A B D H 1 female male 2 2.67 3.6 3 3.38 3.05 4 3.41 3.83 5 3.44 3.66 6 3.79 2.09 7 3.46 2.91 8 2.51 2.53 9 2.85 2.61 10 3.44 3.01 11 3.27 2.36 12 3.54 3.52 13 3.32 2.4 14 2.92 2.52 15 3.89 3.98 16 2.94 3.61 17 3.76 3.11 18 2.93 3.29 ΣAutosum Conditional Formatting Format Cell Insert Delete Format Clear Sort & Find & as Table Styles v Filter Select ▾ Tables Cells Editing K M N Comments Comments Σ AutoSum Conditional Format 0 Formatting as Table M Cell Styles ~ Insert Delete Format Clear Tables Cells Filter Editing Sort & Find & Select File 5 Home Insert Formulas Data Review View Help Tell me what you want to do X Cut AA Copy Paste BIUD ab Format Painter P % 95898 Undo C2 Clipboard Font Alignment Number fx A B D E F G H 1 country1 country2 2 3 4 5 6 7 8 9 10 11 12 13 2222222222 10 9 12 12 11 12 12 15 13 8 13 9 10 10 11 8 13 9 12 11 13 13 12 12 14 11 14 15 14 7 16 11 9 17 13 14 18 11 13 Sheet 1 K L M N о P