Question

I need help with creating the following:

1. Write down a research question.
2. Make sure that your question involves two variables.
3. What variable names are involved with your research question? You can name your variables.
4. Invent 10 data values to describe each of your variables and include the data here.

Answer 1

Hello

1. Write down a research question.

(10 points) A research study younger adults on perceived life hypothesis. Ten older adults ( 30) were give a life satisfaction test on the measure range from° to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below: was conducted to examine the differences between older and satisfaction. A pilot study was conducted to examine this over the age of 70) and ten younger adults (between 20 and known to have high reliability and validity). Scores Older Younger Adults 10Adults 34 38 52 48 25 39 15 27 37 41 24 19 26 36 51 46 46

ANSWER:

Hello,

a) A t-test is used when you're looking at a numerical variable - for example, height - and then comparing the averages of two separate populations or groups (e.g., males and females).

b)

Requirements

• Two independent samples
• Data should be normally distributed
• The two samples should have the same variance

Null Hypothesis

H0: u1 - u2 = 0, where u1 is the mean of first population and u2 the mean of the second.

Older	Diff (X - M)	Sq. Diff (X - M)2
45	0.5	0.25
38	-6.5	42.25
52	7.5	56.25
48	3.5	12.25
25	-19.5	380.25
39	-5.5	30.25
51	6.5	42.25
46	1.5	2.25
55	10.5	110.25
46	1.5	2.25
	M: 44.50	SS: 678.50

Younger	Diff (X - M)	Sq. Diff (X - M)2
34	5.9	34.81
22	-6.1	37.21
15	-13.1	171.61
27	-1.1	1.21
37	8.9	79.21
41	12.9	166.41
24	-4.1	16.81
19	-9.1	82.81
26	-2.1	4.41
36	7.9	62.41
	M: 28.10	SS: 656.90

Difference Scores Calculations

Treatment 1

N₁: 10
df₁ = N - 1 = 10 - 1 = 9
M₁: 44.5
SS₁: 678.5
s²₁ = SS₁/(N - 1) = 678.5/(10-1) = 75.39


Treatment 2

N₂: 10
df₂ = N - 1 = 10 - 1 = 9
M₂: 28.1
SS₂: 656.9
s²₂ = SS₂/(N - 1) = 656.9/(10-1) = 72.99


T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((9/18) * 75.39) + ((9/18) * 72.99) = 74.19

s²_M1 = s²_p/N₁ = 74.19/10 = 7.42
s²_M2 = s²_p/N₂ = 74.19/10 = 7.42

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = 16.4/√14.84 = 4.26

The t-value is 4.25755. The p-value is .000474. The result is significant at p < .05.

Conclusion: there is significant diffreance between the younger and older.

e) the younger and older are two diffrent categories and to compare two indepndent variables we can use two sample t-test for the analysis.

thanks