Question

4. Consider the following research hypothesis and the p-value obtained via a statistical test. Would this testing have involved one-sample or two-sample hypothesis testing? Does the scenario involved paired or independent samples? Assuming the appropriate testing was used, what would be an appropriate conclusion to draw given the reported results and p-value? Explain the reasoning for your answers. The hypothesis is that students who are familiar with the Theory of Algorithms learn the programming language C++ faster than students who are not familiar with this theory. We have gathered data from 30 students who are familiar with the Theory of Algorithms (Group 1) and 30 students who are not familiar with the Theory of Algorithms (Group 2). Experiments showed students from Group 1 took a mean of 32.5 hours to complete the training course of C++, while students Group 2 the mean was 42.1 hours. The p-value was 0.14

Answer 1

Given two samples of students one having a familiarity with Theory of Algorithms , Other not having a familiarity with Theory of Algorithms.

Let S1 : Students having a familiarity with Theory of Algorithms.

S2 : Students not having a familiarity with Theory of Algorithms.

SAMPLE	Mean
S1	32.5
S2	42.1

And the P value = 0.14.

THE TESTING IS A TWO - SAMPLE TESTING AND INVOLVES INDEPENDENT SAMPLES.

THE HYPOTHESIS VALUES FOR THE TESTING

H_{​​​​​​0} (NULL HYPOTHESIS ) : Both the sample of students take same time at learning the c++ language.

H_{​​​​​​1} : Students with a familiarity with Theory of Algorithms learn c++ faster when compared to students with no familiarity with Theory of Algorithms.

The value ( Significance level ) is 0.05 ( Remember the most common choice of significance level is 0.05 ) .

Now clearly p > , Hence the Null Hypothesis is rejected .

( P value less than the significance value is interpreted as indicating evidence of a difference between the population means . That is Null Hypothesis is accepted if > P ).

Since Null Hypothesis is rejected .

H_{​​​​​1} is accepted .

Hence we infer from the above experiment That "Students with familiarity in Theory of Algorithms learn C++ faster than Students with no familiarity in Theory of Algorithms "