please show work so i can understand thank you!! A study was performed to test w
ID: 3055371 • Letter: P
Question
please show work so i can understand thank you!!
A study was performed to test whether cars get better mileage on premium gas than on regular gas. Each of 10 cars was first filled with either regular or premium gas, decided by a coin toss, and the mileage for that tank was recorded. The mileage was recorded again for the same cars using the other kind of gasoline. We want to determine whether cars get significantly better mileage, specifically more than 5mpg, with premium gas at the .05 level. Car # 1 2 3 4 5 6 7 8 9 10 Regular Gas (16, 20, 21, 22, 23, 22, 27, 25, 27, 28) Premium Gas(19, 22, 24, 24, 25, 25, 26, 26, 28, 32) Ho: [a] Ha: [b] Compute the test statistic: [c] and P-value: [d] State your conclusion in the context of the problem: We [e] the null hypothesis. There [f] (is/is not) statistical evidence at the .05 level that cars get more than 5mpg better mileage with premium gas. State a 95% confidence interval for the mean change in gas mileage with premium gas. We are [g]% confident that the mean change in gas mileage is between [h] and [i] with premium gas.Explanation / Answer
a)
H0 : mu1 - mu2 = 5
b)
Ha : mu1 - mu2 >5
c)
x1 = 23.1 , s1 = 3.7253 , x2 = 25.1 , s2 = 3.4464 , n1 = n2 = 10
t= (x1 - x2) - D/sqrt(s1^2/n1 + s2^2/n2)
= ( 23.1 - 25.1 ) - 5/sqrt(3.7253^2/10 + 3.4464^2/10)
= -5.1156
d)
P value = .000036.
e)
we can reject the null hypothesis. There is statistical evidence at the .05 level that cars get more than 5mpg better mileage with premium gas.
g)
t value at 95% = 2.0930
CI = (x1 - x2)+/- t * sqrt(s1^2/n1 + s2^2/n2)
= ( 23.1 - 25.1 ) +/- 2.0930*sqrt(3.7253^2/10 + 3.4464^2/10)
= (-5.3590,1.3590)
We are 95% confident that the mean change in gas mileage is between -5.3590 and 1.3590 with premium gas.
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