If the point (2,-3), then it must satisfy both inequalities.
Let's replace it with the first one
As you can observe, the test point satisfies the first inequality.
Let's evaluate the second one
The test point doesn't satisfy the second inequality.
<h2>Hence, the test point is not a solution to the given system because it doesn't satisfy both inequalities.</h2>Answer:
The slope-intercept form is
Step-by-step explanation:
☆We are going to solve the equation.
☆We are solving for y.
☆All we need to do is divide.
Answer:
Now we just take square root on both sides of the interval and we got:
Step-by-step explanation:
Data given and notation
34,59,61,71,59
We can calculate the sample standard deviation with the following formula:
s=12.021 represent the sample standard deviation
represent the sample mean
n=5 the sample size
Confidence=99% or 0.99
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
The Chi square distribution is the distribution of the sum of squared standard normal deviates .
Calculating the confidence interval
The confidence interval for the population variance is given by the following formula:
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.005,4)" "=CHISQ.INV(1-0.005,4)". so for this case the critical values are:
And replacing into the formula for the interval we got:
Now we just take square root on both sides of the interval and we got:
Answer:
We conclude that the population proportion is equal to 0.70.
Step-by-step explanation:
We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.
Let p = <u><em>population proportion.</em></u>
(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.
(2) So, Null Hypothesis, : p = 0.70 {means that the population proportion is equal to 0.70}
Alternate Hypothesis, : p < 0.70 {means that the population proportion is less than 0.70}
The test statistics that would be used here <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion = 0.63
n = sample of observations = 100
So, <u><em>the test statistics</em></u> =
= -1.528
The value of z-test statistics is -1.528.
<u>Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.</u>
Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.
Therefore, we conclude that the population proportion is equal to 0.70.
(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.