Valeria is playing with her accordion. The length of the accordion A(t)A(t)A, left parenthesis, t, right parenthesis (in \text{c
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Consider a quadratic equation given by
.... (1)
The quadratic formula then is
The quadratic equation provided is
This can be expressed as
.... (2)
By comparing (1) and (2), we derive:
Plug these values into the quadratic formula.
Factoring out common elements.
The two solutions are
and
We recognize that
Thus,
Consequently, root is positive while
is negative.
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!