What is the value of 5 in 42.05
1 answer:
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Answer:
The value of the test statistic is
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
Sample 2:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that
Distribution of the difference:
What is the value of the test statistic?
The value of the test statistic is
Simplify the expression
It can be simplified as below:
The graph of x and y = 4 is symmetric with respect to the line x = y.
Therefore, the answer is the second option shown above, which is:
<span>the line y = x</span>
Below is a graph where you can see the symmetry of xy = 4 with respect to the oblique axis x = y. This axis cuts the curves just at its apex
Therefore, the answer is the second option shown above, which is:
<span>the line y = x</span>
Below is a graph where you can see the symmetry of xy = 4 with respect to the oblique axis x = y. This axis cuts the curves just at its apex