Aresearcher would like to test whether a new teaching method enhances the concept understanding. in a paired sample t test, a random sample of 20 students were given a pre-test before a new method was introduced. after the new method was introduced , a post test was given. the differences of pre-test scores and post test scores ( d = post test score - pre test score) were recorded for all students. the sample mean difference and the standard deviation of differences for the 20 students were 2.82 and 3.7 respectively. what is the value of the t test statistic (for two decimal places) for the paired sample test?

t= 3.41

Step-by-step explanation:

The t test statistic for the paired sample test is given by :-

, where n = sample size.

= sample mean difference for n

= sample standard deviation of differences for n.

Given : The sample mean difference and the standard deviation of differences for the 20 students were 2.82 and 3.7 respectively.

As per given , we have

n=20

Then , the test statistic would be :-

Hence, the  value of the t test statistic for the paired sample test : t= 3.41

its an acute right triangle

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.