- The Table Below Shows The Observed Frequencies For Choice Of Lift Or Stairs When Going Up At A Bus Station At Three Diff 1 (191.16 KiB) Viewed 31 times
- The Table Below Shows The Observed Frequencies For Choice Of Lift Or Stairs When Going Up At A Bus Station At Three Diff 2 (162.9 KiB) Viewed 31 times
- The Table Below Shows The Observed Frequencies For Choice Of Lift Or Stairs When Going Up At A Bus Station At Three Diff 3 (272.53 KiB) Viewed 31 times
The table below shows the observed frequencies for choice of lift or stairs when going up at a bus station at three different times of day. The station manager wishes to determine whether the data provide evidence that the choice for those going up depends on the time of day. Total 426 Lift Stairs Morning-peak 216 210 Off-peak 232 133 Evening-peak 301 213 Total 749 556 365 514 1305 The chi-squared test can be used to check to see if the choice of stairs or lift depends on the time of day. Select the appropriate pair of null and alternative hypotheses for this study: 1 - O Ho : There are differences between the choice of stairs or lift and the time of day. HA: There are no differences between the choice of stairs or lift and the time of day. Ho: Choice of stairs or lift is independent of time of day. HA: Choice of stairs or lift depends on the time of day. O Ho: There is an association between the choice of stairs or lift and the time of day. HA: There is no association between the choice of stairs or lift and the time of day. OH : Choice of stairs or lift depends on the time of day. HA: Choice of stairs or lift is independent of time of day. O Ho : There are no differences between the choice of stairs or lift and the time of day. HA: There is at least one difference between the choice of stairs or lift and the time of day. b) Calculate the expected cell counts for: (1) 05 the "Lift Morning" cell 244.50 ADP the "Stairs/Morning" cell 0.5 181.50 20P the "Lift Off cell 209.49 2DP
b) Calculate the expected cell counts for: the "Lift Morning" cell 0.5 244.50 29P (11) the "Stairs/Morning" cell 05 181.50 2DP the "Lift/Off' cell 05 209.49 2DP 05 (iv) the Stairs Off' cell 155.51 2DP OS the "Lift Evening" cell 295.01 2DP 05 (vi) the "Stairs/Evening" cell 218.99 2DP c) 1 Calculate the x statistic (use your answers from b) in this calculation). IDP 1 d) What are the degrees of freedom for this chi-squared test? 2 e) What line of code gives the p-value for this test? 1 1-pchisqex, 2) Opchisq(X, 1) Opchisq(X², 2) O 1-pchisq(X2, 2, lower.tail=FALSE) Opchisq x², 1, lower.tail=FALSE) f) Select the appropriate conclusion to this hypothesis test given the p-value is less than 0.05; 1 O There is evidence that choice of stairs or lift depends on the time of day, There is evidence of a difference between the choice of stairs or lift and the time of day. O There is insufficient evidence of a difference between the choice of stairs or lift and the time of day.
(1) the "Lift Evening cell 295.01 0.5 (vi) the Stairs Evening" cell 218.99 0.5 । 2DP c) Calculate the x2 statistic (use your answers from b) in this calculation). BE d) What are the degrees of freedom for this chi-squared test? 1 2 ) e) What line of code gives the p-value for this test? 31 1-pchisq', 2) pchisqx?, 1) pchisq(X², 2) 1-pchisq(x², 2, lower tail=FALSE) pchisq(x², 1, lower tail=FALSE) f) Select the appropriate conclusion to this hypothesis test given the p-value is less than 0.05: 1 There is evidence that choice of stairs or lift depends on the time of day. There is evidence of a difference between the choice of stairs or lift and the time of day. O There is insufficient evidence of a difference between the choice of stairs or lift and the time of day. There is insufficient evidence that choice of stairs or lift depends on the time of day. O There is evidence of at least one difference between the choice of stairs or lift and the time of day.