Answer:
Correct option: b 39.
Step-by-step explanation:
A one-sample (or one mean) t-test is applied to test whether the population-parameter is significantly different from some hypothetical value.
The degrees of freedom of the <em>t</em>-test is:
df = n - 1
It is provided that the sample size is, <em>n</em> = 40.
Compute the degrees of freedom as follows:
df = n - 1
= 40 - 1
= 39
Thus, the correct option is b.
Answer:
y = -0.85 + 0.09x; $49.82
Step-by-step explanation:
1. Calculate Σx, Σy, Σxy, and Σx²
The calculation is tedious but not difficult.
![\begin{array}{rrrr}\mathbf{x} & \mathbf{y} & \mathbf{xy} & \mathbf{x^{2}}\\526 & 52.08 & 27394.08 & 276676\\625& 59.00 & 36875.00 &390625\\589 & 56.12 & 33054.68 & 346921\\409 & 25.72 & 10519.48 & 167281\\489 & 34.12& 16684.68 & 293121\\500 & 53.00 & 26500.00 &250000\\906 & 76.48 & 71102.88 & 820836\\251 &26.08 & 6546.08 & 63001\\595 & 50.60 & 30107.00 & 354025\\719 & 68.52 & 49265.88 & 516961\\\mathbf{5609} & \mathbf{503.72} &\mathbf{308049.76} & \mathbf{3425447}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brrrr%7D%5Cmathbf%7Bx%7D%20%26%20%5Cmathbf%7By%7D%20%20%26%20%5Cmathbf%7Bxy%7D%20%26%20%5Cmathbf%7Bx%5E%7B2%7D%7D%5C%5C526%20%26%2052.08%20%26%2027394.08%20%26%20276676%5C%5C625%26%2059.00%20%26%2036875.00%20%26390625%5C%5C589%20%26%2056.12%20%26%2033054.68%20%26%20346921%5C%5C409%20%26%2025.72%20%26%2010519.48%20%26%20167281%5C%5C489%20%26%2034.12%26%2016684.68%20%26%20293121%5C%5C500%20%26%2053.00%20%26%2026500.00%20%26250000%5C%5C906%20%26%2076.48%20%26%2071102.88%20%26%20820836%5C%5C251%20%2626.08%20%26%206546.08%20%26%2063001%5C%5C595%20%26%2050.60%20%26%2030107.00%20%26%20354025%5C%5C719%20%26%2068.52%20%26%2049265.88%20%26%20516961%5C%5C%5Cmathbf%7B5609%7D%20%26%20%5Cmathbf%7B503.72%7D%20%26%5Cmathbf%7B308049.76%7D%20%26%20%5Cmathbf%7B3425447%7D%5C%5C%5Cend%7Barray%7D)
2. Calculate the coefficients in the regression equation
![a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{503.7 \times 3425447 - 5609 \times 308049.76}{10 \times 3425447- 5609^{2}}\\\\= \dfrac{1725466163 - 1727851103.84}{34254470 - 31460881} = -\dfrac{2384941}{2793589}= \mathbf{-0.8537}](https://tex.z-dn.net/?f=a%20%3D%20%5Cdfrac%7B%5Csum%20y%20%5Csum%20x%5E%7B2%7D%20-%20%5Csum%20x%20%5Csum%20xy%7D%7Bn%5Csum%20x%5E%7B2%7D-%20%5Cleft%20%28%5Csum%20x%5Cright%20%29%5E%7B2%7D%7D%20%3D%20%20%5Cdfrac%7B503.7%20%5Ctimes%203425447%20-%205609%20%5Ctimes%20308049.76%7D%7B10%20%5Ctimes%203425447-%205609%5E%7B2%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B1725466163%20-%201727851103.84%7D%7B34254470%20-%2031460881%7D%20%3D%20-%5Cdfrac%7B2384941%7D%7B2793589%7D%3D%20%5Cmathbf%7B-0.8537%7D)
![b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{3080498 - 2825365.48}{2793589} = \dfrac{255132}{2793589} = \mathbf{0.09133}](https://tex.z-dn.net/?f=b%20%3D%20%5Cdfrac%7Bn%5Csumx%20y%20%20-%20%5Csum%20x%20%5Csumxy%7D%7Bn%5Csum%20x%5E%7B2%7D-%20%5Cleft%20%28%5Csum%20x%5Cright%20%29%5E%7B2%7D%7D%20%3D%20%5Cdfrac%7B3080498%20-%202825365.48%7D%7B2793589%7D%20%3D%20%5Cdfrac%7B255132%7D%7B2793589%7D%20%3D%20%5Cmathbf%7B0.09133%7D)
To two decimal places, the regression equation is
y = -0.85 + 0.09x
3. Prediction
If x = 563,
y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85 + 50.67 = $49.82
(If we don't round the regression equation to two decimal places, the predicted value is $50.56.)
I’m sorry I’m late but you multiply that n(x)=200 by x=300 and n(xuy)=400
Answer:
![n=3.875](https://tex.z-dn.net/?f=n%3D3.875)
Step-by-step explanation:
First, we can expand the brackets:
(given)
![-5n+9+3n=-10n+40](https://tex.z-dn.net/?f=-5n%2B9%2B3n%3D-10n%2B40)
(combine like-terms)
![8n=31](https://tex.z-dn.net/?f=8n%3D31)
![n=3.875](https://tex.z-dn.net/?f=n%3D3.875)
Hope this helps :)