Question

How do I do  independent t test on the data set below and how do I know if its pooled t test or unrolled t test?

Health question for reference: to what extend does the age of MI patients vary by gender

Standard deviation: male = 13.944 female= 13.939

mean: male 65.353 female=73.628

Male female

65   88
77   81
78   82
76   66
40   81
83   73
58   64
43   53
39   69
66   67
61   89
49   85
85   81
54   85
82   84
68   83
78   76
56   77
72   84
50   43
75   87
61   70
48   64
82   59
62   91
39   60
45   80
65   72
68   73
73   85
64   80
80   79
74   48
80   32
92   86
51
41
90
83
61
64   
82
48
63
81
52   
65   
74
62
71
73
43
80
72
57
76
53
44
71
64
86
60
63
74
56

Answer 1

Solution:

Here, we have to use two sample t test for the difference between two population means by assuming equal population variances.

We use pooled t test because standard deviations for the given two samples are approximately same and very close to each other.

Null hypothesis: H₀: There is no significant difference in the average age of male and female.

Alternative hypothesis: H_a: There is a significant difference in the average age of male and female.

H₀: µ₁ = µ₂ versus H_a: µ₁ ≠ µ₂

This is a two tailed test.

We assume level of significance = α = 0.05

Test statistic formula for pooled variance t test is given as below:

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

Where S_p² is pooled variance

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

We are given

X1bar = 65.353

X2bar = 73.628

S1 = 13.944

S2 = 13.939

n1 = 65

n2 = 35

df = n1 + n2 – 2 = 65 + 35 – 2= 98

α = 0.05

Critical value = - 1.9845 and 1.9845

(by using t-table)

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

S_p² = [(65 – 1)* 13.944^2 + (35 – 1)* 13.939^2]/(65 + 35 – 2)

S_p² = 194.3868

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

t = (65.353 – 73.628) / sqrt[194.3868*((1/65)+(1/35))]

t = -8.2750 / 2.9231

t = -2.8309

P-value = 0.0056

(by using t-table/excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a significant difference in the average age of male and female.