PLEASE HELP!! What is the scale factor?
1 answer:
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Integration by Parts.
It's not immediately obvious but this numerator differentiates very nicely.
Notice that taking the derivative of the numerator actually creates a factor of our denominator.
Ah ha! So we've found a good choice for our u,
letting dv be everything else.
Applying Integration by parts
gives us,
Simplifying things a little bit before integrating again,
and integrating the last term,
looking for a common denominator, multiplying the first term by 2/2 and the second term by (2x+1)/(2x+1),
Combine the fractions together, factor out the exponential,
combine like-terms as a final step,
and include a constant of integration,
It's not immediately obvious but this numerator differentiates very nicely.
Notice that taking the derivative of the numerator actually creates a factor of our denominator.
Ah ha! So we've found a good choice for our u,
letting dv be everything else.
Applying Integration by parts
gives us,
Simplifying things a little bit before integrating again,
and integrating the last term,
looking for a common denominator, multiplying the first term by 2/2 and the second term by (2x+1)/(2x+1),
Combine the fractions together, factor out the exponential,
combine like-terms as a final step,
and include a constant of integration,
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).