Question

Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data met these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers.

Mary's Study: Mary is planning a study to see if learning of 6th graders on a math lesson is affected by background noise level. She wants to use a t-test for independent groups to analyze her results.

Answer 1

(a) H0: Null Hypothesis: 1 = 2 (Marks obtained by 6th graders on math lesson with high background noise level are the same as marks obtained by 6th graders on math lesson with no background noise level)

HA: Alternative Hypothesis: 1 2 (Marks obtained by 6th graders on math lesson with high background noise level are different from marks obtained by 6th graders on math lesson with no background noise level) (Claim)

(b)

For Intependent t test: Assumption is: (1) Parent population is Normal Distribution. Then only t distribution can be employed. (2) Variances of the two groups are equal in the population.

(c) How would she see if her data met these assumptions: (1) Statistical tests are avaible for testing Normal Distribution to the given data. (2) Levene's Test of Equality of Variances is to be employed.

(d) (1) In case the sample size is large, n > 30, the difference will not be much and hence still can get accurate results from the t -test. Non-parametric test such as the Mann Whitney U test can be used in place of t - test.

(2) In case the population variances are not equal, we cannot use pooled estimate for error term for t test. We have to employ Welch - Satterhwatte method.