An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 138 brakes using Compound 1 yields an average brake life of 30,636 miles. A sample of 111 brakes using Compound 2 yields an average brake life of 43,730 miles. Assume that the population standard deviation for Compound 1 is 3899 miles, while the population standard deviation for Compound 2 is 1161 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Step 1 of 3: Find the point estimate for the true difference between the population means.
Step 2 of 3: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Step 3 of 3: Construct the 95% confidence interval. Round your answers to the nearest whole number.
1)
Point estimate = 1 -
2 = 30636 -
43730 = -13094
2)
Margin of error E = Z * sqrt (
1 / n1 +
2 / n2 )
= 1.96 * sqrt ( 3899 / 138 + 1161 / 111)
= 12.195088
3)
95% confidence interval is
(1 -
2 ) - E <
1
-
2 < (
1 -
2 ) + E
-13094 - 12.195088 < 1 -
2 < -13094 +
12.195088
-13106 < 1 -
2 <
-13082
95% CI is ( -13106 , -13082 )
An investigator compares the durability of two different compounds used in the manufacture of a certain...
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 259 brakes using Compound 1 yields an average brake life of 47,112 miles. A sample of 218 brakes using Compound 2 yields an average brake life of 30,864 miles. Assume that the population standard deviation for Compound 1 is 1681 miles, while the population standard deviation for Compound 2 is 1627 miles. Determine the 98% confidence interval for...
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 259259brakes using Compound 1 yields an average brake life of 47,112 miles. A sample of 218 brakes using Compound 2 yields an average brake life of 30,86430,864 miles. Assume the standard deviation of brake life is known to be 16811681 miles for brakes made with Compound 1 and 1627 miles for brakes made with Compound 2. Determine the 98%98%...
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 259259brakes using Compound 1 yields an average brake life of 47,112 miles. A sample of 218 brakes using Compound 2 yields an average brake life of 30,86430,864 miles. Assume the standard deviation of brake life is known to be 16811681 miles for brakes made with Compound 1 and 1627 miles for brakes made with Compound 2. Determine the...
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 218 students using Method 1 produces a testing average of 58.7. A sample of 243 students using Method 2 produces a testing average of 54.7. Assume that the population standard deviation for Method 1 is 18.63, while the population standard deviation for Method 2 is 16.17. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and...
A researcher compares the effectiveness of two different instructional methods for teaching pharmacology. A sample of 51 students using Method 1 produces a testing average of 81.6. A sample of 76 students using Method 2 produces a testing average of 76.4. Assume that the population standard deviation for Method 1 is 12.24, while the population standard deviation for Method 2 is 11.19. Determine the 90% confidence interval for the true difference between testing averages for students using Method 1 and...
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 59 students using Method 1 produces a testing average of 85.5. A sample of 31 students using Method 2 produces a testing average of 74.4. Assume that the population standard deviation for Method 1 is 19, while the population standard deviation for Method 2 is 7.55. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and...
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 178 178 students using Method 1 produces a testing average of 85.8 85.8 . A sample of 197 197 students using Method 2 produces a testing average of 73.4 73.4 . Assume that the population standard deviation for Method 1 is 5.06 5.06 , while the population standard deviation for Method 2 is 19.39 19.39 . Determine the 95% 95 % confidence interval for...
A researcher compares the effectiveness of two different instructional methods for teaching electronics. A sample of 102 students using Method 1 produces a testing average of 76.4. A sample of 84 students using Method 2 produces a testing average of 62.7. Assume that the population standard deviation for Method 1 is 15.67, while the population standard deviation for Method 2 is 6.76. Determine the 80 % confidence interval for the true difference between testing averages for students using Method 1...
A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 169 students using Method 1 produces a testing average of 81.7. A sample of 128 students using Method 2 produces a testing average of 72.5. Assume the standard deviation is known to be 5.87 for Method 1 and 17.66 for Method 2. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2....
Given two independent random samples with the following results: ni = 15 n2 = 13 Xi = 153 X2 = 114 $i = 19 S2 = 21 Use this data to find the 95 % confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Copy Data Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round...