Given:
The system of equations is
To find:
The true statement about the given system of equations.
Solution:
The slope intercept form of a line is
Where, m is the slope and b is the y-intercept.
We have,
On comparing these two lines with slope intercept form, we get
Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.
Therefore, the correct option is A.
Answer:
We conclude that the mean waiting time is less than 10 minutes.
Step-by-step explanation:
We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.
Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.
Let = <u><em>mean waiting time for bus number 14.</em></u>
So, Null Hypothesis, :
10 minutes {means that the mean waiting time is more than or equal to 10 minutes}
Alternate Hypothesis, :
< 10 minutes {means that the mean waiting time is less than 10 minutes}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean waiting time = 7.8 minutes
s = sample standard deviation = 2.5 minutes
n = sample of different occasions = 18
So, <u><em>test statistics</em></u> = ~
= -3.734
The value of t test statistics is -3.734.
Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.
Since our test statistic is less than the critical value of t as -3.734 < -2.567, 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 waiting time is less than 10 minutes.