A local college is forming a seven-member research committee having one administrator, three faculty members, and three students
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Answer:
The critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998.
The test statistic (t=1.729) is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.
At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.
Step-by-step explanation:
We have a matched-pair t-test for the difference.
We have the null and alternative hypothesis written as:
We have n=8 pairs of data. We calculate the difference as:
Then, with this procedure we get the sample for d:
The sample mean and standard deviation are:
Now, we can perform the one-tailed hypothesis test.
The significance level is 0.01.
The sample has a size n=8.
The sample mean is M=7.25.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.86.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a right-tailed test, with 7 degrees of freedom and t=1.729, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0637) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.
If we use the critical value approach, the critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998. The test statistic is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.
Answer:
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
Step-by-step explanation:
In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...
A = 1/2bh
where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.
You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.
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For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).
In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.
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The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
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By way of example, we can "show work" for problem 1:
1. S = Ph +2B
S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2
