A magazine publisher is studying the influence of type style and darkness on the readability of her
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There are two factors A type style and B type darkness We will apply twoway analysis of variance with two observations per cell The Minitab printout is shown below Factor means and confidence intervals for factor levels are included Twoway ANOVA Seconds versus Style Darkness Analysis of Variance for Seconds Source DF SS MS F P Style 1 1200 1200 225 0184 Darkness 2 6450 3225 605 0036 Interaction 2 950 475 089 0458 Error 6 3200 533 Total 11 11800 Individual 95 CI Style Mean 1 2800 2 2600 2400 2560 2720 2880 Individual 95 CI Darkness Mean 1 303 2 250 3 258 240 270 300 330 Using Minitab we can also generate the cell means along with the factor level means Tabulated Statistics Style Darkness Rows Style Columns Darkness 1 2 3 All 1 30500 25500 28000 28000 2 30000 24500 23500 26000 All 30250 25000 25750 27000 Cell Contents SecondsMean The data setup and a portion of the Excel printout are shown below Testing for Main Effects Factor A type style H 0 a i 0 for each value of i i 1 through 2 H 1 a i 0 for at least one value of i The calculated test statistic is F 2250 The pvalue is 0184 which is not a 005 Do not reject H 0 At the 005 level none of the type styles has any effect on readability Testing for Main Effects Factor B type darkness H 0 b j 0 for each value of j j 1 through 3 H 1 b j 0 for at least one value of j The calculated test statistic is F 6047 The pvalue is 0036 which is a 005 Reject H 0 At the 005 level at least one of the levels of type darkness has an effect on readability Testing for Interaction Effects H 0 a b ij 0 for each combination of i and j H 1 a b ij 0 for at least one combination of i and j The calculated test statistic is F 0891 The pvalue for this test is 0458 which is not a 005 Do not reject H 0 At the 005 level there is no relationship between type style and type darkness For a confidence level of 95 the righttail area of interest is 1 0952 0025 with df 6 Referring to the t table t 2447 MSE 5333 and its square root 2309 is the estimate for the population standard deviation The 95 confidence interval ...View the full answer
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