A distributor of personal computers has five locations in a city. In the year's first quarter, the sales in units were: Location
Observed Sale ( units) Northside 70 Pleasant Township 75 Southwick 70 I-90 50 Venice Avenue 35 Total 300 For a goodness-of-fit test that sales were the same for all locations, what is the critical value at the 0.01 level of risk? Select one: a. 7.779 b. 15.033 c. 13.277 d. 5.412
1 answer:
Answer:
The correct option is (c) 13.277.
Step-by-step explanation:
The observed data is:
Location Observed sales (units)
Northside 70
Pleasant Township 75
Southwick 70
I-90 50
Venice Avenue 35
TOTAL 300
The test statistic for the Goodness of fit test is:
For <em>k</em> independent samples this test statistic follows a Chi-square distribution with degrees of freedom (<em>k</em> - 1).
The sample size in this case is, <em>k</em> = 5.
The degrees of freedom is, (<em>k</em> - 1) = 4.
The level of significance is, <em>α</em> = 0.01.
The critical value of the test is:
**Use the Chi-square table.
Thus, the critical value is 13.277.
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9514 1404 393
Answer:
63.7% or 33.35 miles
Step-by-step explanation:
The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.
The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...
y/38 +x/36 = 1
19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount
Then the distance from the origin to the line is ...
d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243
The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:
x² + (26.1243)² = 31²
x² = 31² -(684/√685)² = 190429/685
x ≈ 16.6733
The driving distance for which the transmitter is picked up is twice this, so is ...
2x = 2(16.6733) ≈ 33.3466 . . . miles
The total drive length is also given by the Pythagorean theorem:
drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles
Then the fraction of the drive during which the signal is picked up is ...
fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%
__
The signal is picked up for 33.35 miles, about 63.7% of the drive.
______
The intercept-form equation for a line is ...
x/(x-intercept) +y/(y-intercept) = 1
The distance from (x, y) to line ax+by+c=0 is given by ...
d = |ax+by+c|/√(a²+b²)
The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:
c² = a² +b²
Answer:
Tj should write 5.75 hours on her time card.
Step-by-step explanation:
We have been given, Tj worked for 5 hours and 45 minutes.
We will convert 45 minutes to hours by dividing 45 by 60 as one hour has 60 minutes.
=0.75 hours
Hence, Tj should write 5.75 hours on her time card.