10) through: (3.-1). slope = -1
1 answer:
Answer:
Step-by-step explanation:
The question is to find the equation of the line going through the points (3,-1) and has a slope of -1.
First, the equation of a line is given as:
Equation = y = mx + b
Where
m is the slope
b is the y-intercept (y-axis cutting point)
We know the slope, so the equation becomes:
y = mx + b
y = -1x + b
y = -x + b
Now the point given is in the form (x,y), so
x = 3
y = -1
We substitute and find b:
y = -x + b
-1 = -3 + b
-1 + 3 = b
b = 2
Final Equation:
y = -x + 2
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Answer:
We conclude that this is an unusually high number of faulty modems.
Step-by-step explanation:
We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.
The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.
Let p = <em><u>population proportion</u></em>.
So, Null Hypothesis, : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}
Alternate Hypothesis, : p > 0.013 {means that this is an unusually high number of faulty modems}
The test statistics that would be used here <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion faulty modems=
= 0.027
n = sample of modems = 367
So, <u><em>the test statistics</em></u> =
= 2.367
The value of z-test statistics is 2.367.
Since, we are not given with the level of significance so we assume it to be 5%. <u>Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.</u>
Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.
Therefore, we conclude that this is an unusually high number of faulty modems.