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Answer:
(a) The test statistic value is -1.83.
(b) We accept the null hypothesis at α = 0.01.
Step-by-step explanation:
The information provided is:
The hypothesis is defined as follows:
<em>H₀</em>: <em>μ</em> ≥ 130 versus <em>Hₐ</em>: <em>μ</em> < 130.
Since the population standard deviation is provided, we will use a z-test.
Compute the test statistic as follows:
The test statistic value is -1.83.
(b)
Compute the p-value of the test as follows:
p-value = P (Z < -1.83)
= 0.034
* Use a z-table.
We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.
• p-value = 0.034 < α = 0.04. Reject the null hypothesis.
• p-value = 0.034 > α = 0.01. Fail to reject the null hypothesis.
• p-value = 0.034 < α = 0.05. Reject the null hypothesis.
• p-value = 0.034 < α = 0.10. Reject the null hypothesis.
Given:
The given equation of line is
To find:
The equation of line that passes through (-5,4) and is parallel to the given line.
Solution:
Slope intercept form of a line is
...(i)
where, m is slope and b is y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Slope of given line is .
Slope of parallel lines are same. So, slope of parallel line is .
The required line passes through (-5,4) with slope . So, the equation of line is
Adding 4 on both sides, we get
Therefore, the correct option is a.