Question

12. What is the average value expected for the independent-measures t statistic if the null hypothesis is true? a. O b. 1 C. 41 d. Mi-M2 13. For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (HA)? a. There are no differences between any of the population means b. At least one of the three populations means is different from another mean C. All three of the population means are different from each other d. None of the above choices are correct 14. When comparing more than two treatment means, why should you use an analysis of variance instead of using severalt tests? a. Using severalt tests increases the risk of a Type I error b. Using severalt tests increases the risk of a Type Il error C. The analysis of variance is more likely to detect a treatment effect d. There is no advantage to using an analysis of variance instead of several t tests

Answer 1

Solution:

12. expected for the t statistic when the null hypothesis is true is:

We reject null hypothesis when

           t > t critical

We know that t critical value is based on sample size and level of significance,

under null hypothesis , test statistic follows t distribution.

The mean of t distribution is zero.

So, the expected value is 0

i.e

Null hypothesis, ho: population mean, u = sample mean, Xbar

Alternative hypothesis, h1: population mean, u =/= sample mean, Xbar

Test statistic, t = (Xbar-u)/(sd/sqrt(n))

Under the assumption that null hypothesis is true, u = Xbar, hence test statistic is, t = 0

so, On average, the value is 0(zero) expected for the t statistic when the null hypothesis is true.

Hence,

option(a) is correct

(a):0