A statistician wants to determine if there is a difference in the fuel efficiency of cars between model years. To do this, he se
lects random makes and models of cars and compares the fuel efficiency in miles per gallon of the current model year and the previous model year. Suppose that data were collected for a random sample of 9 cars, where each difference is calculated by subtracting the fuel efficiency in miles per gallon of the previous model year from the fuel efficiency in miles per gallon of the current model year. Assume that the fuel efficiencies are normally distributed. The statistician uses the alternative hypothesis Ha:μd≠0. Using a test statistic of t≈6.163, which has 8 degrees of freedom, determine the range that contains the p-value.
1 answer:
Answer:
P-value = 0.00028
Step-by-step explanation:
The statician performs an hypothesis test for the mean difference.
As the alternative hypothesis is<em> Ha: μd ≠ 0</em>, we know that it is a two-tailed test.
The test statistic is t=6.163.
For a two-tailed test and 8 degrees of freedom, this corresponds to a P-value of:
This P-value is smaller enough to reject the null hypothesis at almost any significance level.
You might be interested in
Answer:
a)
The variance is given by:
And the deviation is just the square root of the variance and we got:
b)
And for this case we can use the cumulative distribution given by:
And replacing we got:
Step-by-step explanation:
For this case we assume that X is our random variable and we know that the distribution for X is given by:
Part a
For this case the expected value is given by:
The variance is given by:
And the deviation is just the square root of the variance and we got:
Part b
For this case we want to find this probability:
And for this case we can use the cumulative distribution given by:
And replacing we got:
I am assuming that your function is
due to the fact you did not write x-1
the domain is the numbers you can use for x without getting wierd results
wierd results happen when you divide by 0 or take the square root of a negative number
the arean't any division signs so no division by 0
but there is a square root sign
so the part under the square root must be greater than or equal to 0
find where it is equal to 0
0=x+6
minus 6
-6=x
when x is smaller than -6, we get undefined because we get square root of a negative
so the domain (numbers you can use for x) is D={x|x≥-6} or basically x≥-6
the domain is the numbers you can use for x without getting wierd results
wierd results happen when you divide by 0 or take the square root of a negative number
the arean't any division signs so no division by 0
but there is a square root sign
so the part under the square root must be greater than or equal to 0
find where it is equal to 0
0=x+6
minus 6
-6=x
when x is smaller than -6, we get undefined because we get square root of a negative
so the domain (numbers you can use for x) is D={x|x≥-6} or basically x≥-6