PROBLEM 1 The mileage (the distance a car can travel on one liter of gasoline) o

Question

PROBLEM 1 The mileage (the distance a car can travel on one liter of gasoline) of a car is measured. Historically, it is known that the measurement technique has a standard deviation of 1 kilometer (the result is random due to the influence of air temperature and wind, tire types, etc.) and produces results that are normally distributed with zero mean error. Twenty five measurements were made and the average value of 12 km/l was obtained I. Find the 90% and 95% confidence intervals for the mileage. 2. What is the confidence level of the confidence interval [11.5, 12.5] km/li? 3. How many measurements should be made in order to obtain the margin of error no more than 0.2 km at the 99% confidence level?

Explanation / Answer

Solution1;

given sample mean=12

population standard deviation=1

n=25

z crit for 90%=1.645

90% confidence inetrval for mean is

sample mean-zcrit(pop stddev/sqrt(n),sample mean+zcrit(pop stddev/sqrt(n)

12-1.645(1)/sqrt(25),12+1.645(1)/sqrt(25)

11.671,12.329

lower limit=11.7

upper limit=12.3(to one decimal)

90% confidence interval for mean are 11.7 and 12.3

z crit for 95%=1.96

2-1.96(1)/sqrt(25),12+1.96(1)/sqrt(25)

11.608,12.392

lower limit=11.6

upper limit=12.4

95% confidence interval for mean are 11.6 and 12.4

Solution2:

z crit for 99%=2.576

2-2.576(1)/sqrt(25),12+2.576(1)/sqrt(25)

11.4848, 12.5152

11.5,12.5

lower limit=11.5

upper limit=12.5

99% confidence interval for mean are 11.5 and 12.5

Given confidence level is 99%

Solution3:

n=sample size required

n=(Zc*sigma/E)^2

Zc for 99%=2.576

n=(2.576*1/0.2)^2

n=165.8944

n=166

required sample szie=166

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