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Option b is true to match the vector field f with the given plot f(x, y)=x, -y
<h3>What is meant by a function?</h3>The earliest known attempts at the concept of functions can be traced back to the work of the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were idealized dependencies of one variable on another. For example, planetary positions are functions of time. Historically, this concept was developed in calculus towards the end of his 17th century, and the functions studied were differentiable (i.e. they had a high degree of regularity) until his 19th century ).
Given,
f(x, y) = x, -y
gt; at x⇒∞, y⇒-∞ downwards
at x⇒∞, y⇒+∞ downwards
Therefore, option b is true to match the vector field f with the given plot
f(x, y)=x, -y
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The complete question is as follows:
Match the vector field f with the correct plot. f(x, y) = x, −y
3)
Assuming that the population of the study has a normal distribution and that you are studying the population mean μ.
The statistic hypotheses are
If you look at the alternative hypotheses, it includes the symbol "<", which indicates that the test is <em>one-tailed</em>. This means that you will reject the null hypotheses at small values of the test statistic.
Since the sample size is small (n=4) and the given sample data. The test statistic to use for the test is the Student's t:
To calculate the value of the statistic under the null hypothesis you have to use the sample data and the value of the population mean under the null hypothesis:
μ= 87.8
sample mean= 75
sample standard deviation= 17.1
n=4
The test statistic under the null hypothesis is -1.497
The p-value is the probability corresponding to the calculated statistic if possible under the null hypothesis.
So you have to calculate the probability of obtaining the value t=-1497
The student t has n-1 degrees of freedom, since the sample taken is n=4, the degree of freedom is 3.
The p-value is then the accumulated probability up to -1.497 under a t-distribution with 3 degrees of freedom:
The p-value is equal to 0.1157
4)
To make a decision using the p-value, you have to compare the said value with the level of significance, following the decision rule:
- If the p-value ≥ α, do not reject the null hypothesis.
- If the p-value < α, reject the null hypothesis.
The p-value (0.1157) is greater than the significance level (α= 0.05)
The decision is "do not reject the null hypothesis."
