Which graph represents the function below? (The first pic is the function, the others are the graph choices given)
1 answer:
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Answer:
a) The null and alternative hypothesis are:
Test statistic t=0.88
The P-value is obtained from a t-table, taking into acount the degrees of freedom (419) and the type of test (two-tailed).
b) A P-value close to 1 means that a sample result have a high probability to be obtained due to chance, given that the null hypothesis is true. It means that there is little evidence in favor of the alternative hypothesis.
c) The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).
d) The consequences of the confidence interval containing 0 means that the hypothesis that there is no difference between the response time (d=0) is not a unprobable value for the true difference.
This relate to the previous conclusion as there is not enough evidence to support that there is significant difference between the response time, as the hypothesis that there is no difference is not an unusual value for the true difference.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that there is significant difference in the time response for the two servers.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.
The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.
The difference between sample means is Md=0.3.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this test are:
This test is a two-tailed test, with 419 degrees of freedom and t=0.88, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.381) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.
<u>Confidence interval </u>
We have to calculate a 95% confidence interval for the difference between means.
The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.
The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.
The difference between sample means is Md=0.3.
The estimated standard error of the difference is s_Md=0.342.
The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).
The approximate area of the park on the grid is: E. about 40 km² to 50 km².
<h3>How to Find the Approximate Area on a Coordinate Grid?</h3>The number of square on a coordinate grid that is covered determines the area covered. We can make an estimate by counting how many of this square on the coordinate grid that is covered, then find out the area depending on how much square area each grid represents.
In the coordinate plane given, which shows a park, we are told that each of the square on the grid equals 1 k = square kilometer.
The number of each of these squares we can find that is covered by the park on the grid is: 48 squares.
Therefore, the area of 48 squares on the grid = 48 × 1 = 48 km². Since not all squares are fully covered by the park, we can state that the approximate area of the park on the grid is: E. about 40 km² to 50 km².
Learn more about the approximate area on a grid on:
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