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Sagot :
The t-statistic for these two sample is 3.80 with 73 df
T-value is a ratio of the difference between the mean of two samples sets an the variation exist within the sample sets .
The numerator value is difference of mean of two samples.
According to the question,
We have two different sample
Sample 1
n1 = 35 (sample size)
x1 = 13.6 (sample mean)
s1 = 5.8 (standard deviation)
Sample 2
n2 = 40
x2 = 10.1
s2 = 8.5
To calculate the t-value of difference of sample means
[tex]t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{s_1^2}{n_1} - \frac{s_2^2}{n_2}}}[/tex]
Substituting all the values
=> [tex]t = \frac{13.6-10.1}{\sqrt{\frac{5.8^2}{35} - \frac{8.5^2}{40}}}[/tex]
Solving ,
=> t = 3.5 / 0.9192
=> t = 3.807
With degree of freedom = n1 + n2 - 2
=> df =73
To know more about t-statistics here
https://brainly.com/question/28000141
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