multiple choice The number of degrees of freedom for the denominator in one-way
ID: 3253238 • Letter: M
Question
multiple choice The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is: 60 19 56 45 In one-way ANOVA, the term x refers to the: sum of the sample means. sum of the sample means divided by the total number of observations. sum of the population means. weighted average of the sample means. For which of the following not a required condition for ANOVA? The populations are normally distributed. The population variances are equal. The samples are independent. All of these choices are required conditions for ANOVA. One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances. Which of the following is the null hypothesis for this procedure? mu_1 + mu_2 + mu_3 = 0 mu_1 + mu_2 + mu_3 notequalto 0 mu_1 = mu_2 = mu_3 = 0 mu_1 = mu_2 = mu_3 In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the number of degrees of freedom for error is: k-1 n - k n - 1 n - k + 1 In one-way analysis of variance, between-treatments variation is measured by the: SSE SST SS(Total) standard deviation One-way ANOVA is applied to independent samples taken from four normally distributed populations with equal variances. If the null hypothesis is rejected, then we can infer that all population means are equal. all population means differ. at least two population means are equal. at least two population means differ. Consider the following partial ANOVA table: The numerator and denominator degrees of freedom for the F-test (identified by asterisks) are 4 and 15 3 and 16 15 and 4 16 and 3Explanation / Answer
Q>11 Degree of freedom in denominator = 15 *4 - 4 = 56 (option c)
Q.12 The term xbar-bar is the sum of the sample means divided by total number of observations.
Q.13 All of these choices are required conditions for ANOVA (option D)
Q.14 Null Hypoyhesis : 1 = 2 = 3 (option D)
Q.15 The number of degrees of freedom of error is n-k (option b)
Q.16 Between Treatments variation is SSE (optioon A)
Q.17 if null hypothesis is rejected than at least two population means are different.
Q. 18 Here F = 6.67
MST/MSE = F = 6.67
MST = 3.75 * 6.67 = 25
df(treatments ) = 75/25 = 3
so df (errror) = 19 - 3 = 16
so Answer is option b.
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