If the null space of a 4 x 9 matrix is 5-dimensional, what is the dimension of the column space of the matrix? Explain your answ
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Answer:
The degrees of freedom are
And the p value is given by:
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where t follows a t distribution with degrees of freedom and the pooled variance
is given by this formula:
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
We have the following data given:
represent the sample size for group 1
represent the sample size for group 2
represent the sample mean for the group 1
represent the sample mean for the group 2
represent the sample standard deviation for group 1
represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
And the deviation would be just the square root of the variance:
The statistic is givne by:
The degrees of freedom are
And the p value is given by:
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different