There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the
1 answer:
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Answer:
A. Yes, overdetermined systems can be consistent.
As, the system of equations below is consistent because it has a solution
,
,
.
Step-by-step explanation:
We have,
'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.
For e.g. Let us consider the system,
2x - 3y = 1
3x - 2y = 4
x - y = 1
Plotting these equations, we see from the graph below that,
The only intersection point is (2,1). Thus, x= 2 and y= 1 is the solution of this system.
Thus, over-determined system can be consistent.
According to the options,
Option C is not correct as,
,
implies
.
Hence, option A is correct.
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.