Question

R Functions Values Table 1: (Normal distribution) The results in Columns 2 and 4 are the output from an R command, specified in the column header. Columns 2 is pnorm() calls of inputs in Column 1, and Columns 4 is qnorm() calls of inputs in Column 3. Input q pnorm(q, lower.tail = TRUE) -2.577 0.0049 -1.438 0.0752 -1.053 0.1462 -2.920 0.0018 Input p qnorm(p, lower tail = TRUE) 0.01 2.326 0.005 2.576 0.05 1.6.15 0.025 1.960 Table 2: (t-distribution) Each of the results in columns 2-4 is the output from an Rcommand: pt(q, df = ??, lower tail = FALSE) and qt(p, df = ??, lover.tail = FALSE) with degrees-of-freedom, df, given by the column headers. Input q df = 5 de 7 df=18 2.577 0.02418 0.0183 0.0095 1.438 0.1050 0.0968 0.0838 1.053 0.1703 0.1637 0.1531 2.920 0.0165 0.0111 0.00-16 Input p df = 5 df= 7 df= 18 0.005 4.032 3.500 2.878 0.025 2.571 2.365 2.101 0.05 2.015 1.895 1.734 (1) (Hypothetical problem) Two friends in MATH 1052H class were arguing whether learning the R programming languages helps in landing a professional job in the future. To settle their dispute, they decided to make a hypothesis test at 1% significance level and took two independent samples of 50 alumni who learned R some time in their degree program and 40 alumni who never learned R at any point in their degree program. Of the 50 alumni who learned R in their degree program, 37 said that they landed their first professional job within a year. Of the 40 alumni who never learned R at any point in their degree program, 19 said that they landed their first professional job within a year. Answer the following questions. (a) Identify the two populations. (b) State the null and alternative hypotheses. (c) Compute the value of the test statistics. (a) Find the p-value (e) State your decision. (f) At 1% significance level, do the data support that learning R programming language helps landing a professional job in the future. Table 3: (x-distribution) Each of the results in columns 2-4 is the output from an R command: pchisq(q, df = ??, lower tail - FALSE) and qchisq(p, df - ??, lower tail - FALSE) with degrees-of-freedom, df, given by the column headers. Input q df = 5 df= 7 df= 18 2.577 0.7649 0.92121 1.438 0.9201 0.9844 1 1.053 0.9582 0.9939 1 2.920 0.7123 0.8923 1 Input pdf = 5 df= 7 df= 18 0.005 4.032 3.500 2.878 0.025 2.571 2.365 2.101 0.05 2.015 1.895 1.734