Question

In a study, it is wondered if there is a difference between the number of characters used by Generation Y
and Generation Z in the posts they share on social media. The data from 9 random samples selected from
both groups are given below.
Generation Y: 80 70 81 83 74 73 100 79 84
Generation Z: 61 64 66 68 74 72 70 80 63
Conduct a hypothesis test to determine if the Generation Z use more characters than Generation Y when
post on social media. Use a significance level of 0.05.
a. Test the hypothesis using a suitable Parametric test. (15 points)
b. Test the hypothesis using a Non-Parametric test. Prefer the more powerful non-parametric test. (15
points)
Compare test results with test results in question a.

Answer 1

Answer A:

Parametric test.

We can assume that there is a normal distritbution for genration of Y and Z

Null hypothesis : the character used by Z is less than or eqaul to character used by Y

Alternatively hypothesis : the character used by Z is greater than character used by Y

so mean of the Y is 80.44 character and mean of the Z is 68.67 characters.

Standard deviation of the Y is 8.733 and Z is 6.020

Standard error of the Y is 2.911 and for Z is 2.006

If we have two sample t test

t = (uZ -uY )/(standard error of Z+ standard error of Y)

t =(68.67-80.44)/(2.911+2.006)

t =2.3974

If we calculate the critical value of t at 16 (9-1+9-1) degree of freedom is 1.74589

So calcuated t value is higher than the critical t value so we can reject the null hypothesis and accept the alternate hypothesis.

So we can say that character used by Z is more than character used by Y