Hello! You need to calculate a 99% confidence interval for the difference in mean lifespan between two tire brands. Each tested car was assigned one tire from each brand randomly on the rear wheels, allowing for paired sample analysis.
Brand 1 Brand 2 X₁-X₂
car 1: 36,925; 34,318; 2.607
car 2: 45,300; 42,280; 3.020
car 3: 36,240; 35,500; 0.740
car 4: 32,100; 31,950; 0.150
car 5: 37,210; 38,015; -0.0805
car 6: 48,360; 47,800; 1.160
car 7: 38,200; 37,810; 0.390
car 8: 33,500; 33,215; 0.285
n= 8
The study variable is defined as Xd= X₁-X₂, where X₁ represents the tire lifespan (in km) from Brand 1 and X₂ represents Brand 2. Thus, Xd is the difference in tire lifespan.
Xd~N(μd;δd²) (normality test p-value is 0.4640).
For calculating the confidence interval, the best statistic is the Student's t using the following formula:
t= (xd[bar] - μd)/(Sd/√n) ~t₍ₙ₋₁₎
sample mean: xd[bar]= 0.94
standard deviation: Sd= 1.29
= 3.355
xd[bar] ±
*(Sd/√n) ⇒ 0.94 ± 3.355*(1.29/√8)
[-0.65;2.54]km.
The CI can be compared to bilateral hypothesis testing:
H₀:μd=0
H₁:μd≠0
using significance level of 0.01.
Since the confidence interval includes zero, we do not reject the null hypothesis, indicating no significant difference between the tire brands.
Hope you have a fantastic day!
Answer:
An eight-digit grid coordinate allows for precision within 10 meters.
Step-by-step explanation:
Grid coordinates are designed to direct accurately to a specific location by using a map that includes equally spaced vertical and horizontal lines, each assigned numbers to outline a place. The intersection of these vertical and horizontal lines has unique identifiers and creates small sections called grid squares.
The precision increases with the number of digits in the coordinate; an eight-digit designation gives accuracy to the nearest 10 meters.
Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line.
Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.
15x + 10y ≥ 1,100
15(0) + 10(0)? 1,100
0? 1,100
0 < 1,100
This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.
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