There are 20 students in a drama class. The mean age of 12 students is 18 years. The mean age of the remaining 8 students of the
1 answer:
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Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is
Answer:
We conclude that the mean commute time in the U.S. is less than half an hour.
Step-by-step explanation:
We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.
In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.
Let = <u><em>mean commute time in the U.S..</em></u>
So, Null Hypothesis, :
30 minutes {means that the mean commute time in the U.S. is more than or equal to half an hour}
Alternate Hypothesis, :
< 30 minutes {means that the mean commute time in the U.S. is less than half an hour}
The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample mean commute time = 27.6 minutes
s = sample standard deviation = 19.6 minutes
n = sample of people from the 2000 U.S. Census = 500
So, <u><em>the test statistics</em></u> = ~
= -2.738
The value of t test statistic is -2.738.
Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.</u>
Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis.</u>
Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.