Respuesta :
Answer:
The degrees of freedom is 11.
The proportion in a t-distribution less than -1.4 is 0.095.
Step-by-step explanation:
The complete question is:
Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the proportion in a t-distribution less than -1.4 if the samples have sizes 1 = 12 and n 2 = 12 . Enter the exact answer for the degrees of freedom and round your answer for the area to three decimal places. degrees of freedom = Enter your answer; degrees of freedom proportion = Enter your answer; proportion
Solution:
The information provided is:
[tex]n_{1}=n_{2}=12\\t-stat=-1.4[/tex]
Compute the degrees of freedom as follows:
[tex]\text{df}=\text{Min}.(n_{1}-1,\ n_{2}-1)[/tex]
[tex]=\text{Min}.(12-1,\ 12-1)\\\\=\text{Min}.(11,\ 11)\\\\=11[/tex]
Thus, the degrees of freedom is 11.
Compute the proportion in a t-distribution less than -1.4 as follows:
[tex]P(t_{df}<-1.4)=P(t_{11}<-1.4)[/tex]
[tex]=P(t_{11}>1.4)\\\\=0.095[/tex]
*Use a t-table.
Thus, the proportion in a t-distribution less than -1.4 is 0.095.
The proportion in a t-distribution less than -1.4 is 0.095 and this can be determined by using the given data.
Given :
- Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means.
- The samples have sizes [tex]\rm n_1[/tex] = 12 and [tex]\rm n_2[/tex] = 12.
- T statistics = -1.4
The degree of freedom is given by:
[tex]\rm df=Min.(n_1-1,n_2-1)[/tex]
[tex]\rm df=Min.(12-1,12-1)[/tex]
df = Min.(11 , 11)
df = 11
Now, compute the proportion in t-distribution:
[tex]\rm P(t_{df}<-1.4) = P(t_{11}<-1.4)[/tex]
[tex]\rm = P(t_{11}>1.4)[/tex]
= 0.095
The proportion in a t-distribution less than -1.4 is 0.095 and this can be determined by using the given data.
For more information, refer to the link given below:
https://brainly.com/question/16944173
