Dylan jones kept careful records of the fuel efficiency of his new car. after the first eleven times he filled up the tank, he found the mean was 25.7 miles per gallon (mpg) with a sample standard deviation of 0.9 mpg. compute the 95% confidence interval for his mpg

Step-by-step explanation:

As per  given , we have

n=11

df = 11-1=10

Since population standard deviation is unknown , so we use t-test.

Critical t-value :

Confidence interval for population mean :_

Hence, the  95% confidence interval for his mpg =

14

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt