There is a geometric theorem that says "If two lines in a plane are
1 answer:
Answer:
Step-by-step explanation:
For a line to be perpendicular to another line, its slope must be the negative inverse of the original line’s.
For example, the negative inverse of 3x is -1/3 x.
The line y = 3x is perpendicular to y = -1/3 x. Any line with a slope of 3x is perpendicular regardless of its y-intercept.
Plotted on the graph are the equations:
Y = 3x
Y = 3x + 3
Y = - 1/3 x
As you can see, the lines with the slope of 3x are perpendicular to the third line regardless of their y-intercepts. Only slope matters in regards to parallel and perpendicular lines.
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Answer:
Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.
Step-by-step explanation:
We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.
So, firstly according to Central limit theorem the z score probability distribution for sample means is given by;
Z = ~ N(0,1)
where, = average age of the random sample of horses with colic = 12 yrs
= average age of all horses seen at the veterinary clinic = 10 yrs
= standard deviation of all horses coming to the veterinary clinic = 8 yrs
n = sample of horses = 60
So, probability that a sample mean is 12 or larger for a sample from the horse population is given by = P(
12)
P(
12) = P(
) = P(Z
1.94) = 1 - P(Z < 1.94)
= 1 - 0.97381 = 0.0262
Therefore, probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is given as :
We know quotient identity as :
Similarly, we know reciprocal identity as :
lets plug the value of cot and sec in given expression
cos will be cancelled, remaining will be
Using reciprocal identity again, that will equal to :
................... Answer (A)
Answer:
If we compare the p value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.
Step-by-step explanation:
1) Data given and notation
n=500 represent the random sample taken
X=380 represent the number of people with some characteristic
estimated proportion of adults that said that it is morally wrong to not report all income on tax returns
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.
b) The sample needs to be large enough
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
If we compare the p value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.