Respuesta :
Answer:
"=T.INV(0.95,24)" and we got [tex] t_{crit}=+1.711[/tex]
b. +1.711
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
This last one is an unbiased estimator of the common variance [tex]\sigma^2[/tex]
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]
Or equivalently:
Null hypothesis: [tex]\mu_1 - \mu_2 \leq 0[/tex]
Alternative hypothesis: [tex]\mu_1 -\mu_2 > 0[/tex]
Our notation on this case :
[tex]n_1=13[/tex] represent the sample size for group 1
[tex]n_2 =13[/tex] represent the sample size for group 2
[tex]\bar X_1 [/tex] represent the sample mean for the group 1
[tex]\bar X_2[/tex] represent the sample mean for the group 2
[tex]s_1[/tex] represent the sample standard deviation for group 1
[tex]s_2[/tex] represent the sample standard deviation for group 2
Now we can calculate the degrees of freedom given by:
[tex]df=13+13-2=24[/tex]
Since is a right tailed test we need to look on the t distribution with 24 degrees of freedom that accumulates 0.05 of the area on the right. And we can use the following excel code:
"=T.INV(0.95,24)" and we got [tex] t_{crit}=+1.711[/tex]
b. +1.711
Answer:
D. +2.064
Step-by-step explanation:
Total number of samples = 13+13 =26, degree of freedom = 26 - 2 = 24
t-value (critical value) corresponding to 24 degrees of freedom and 0.05 significance level is +2.064
