Construct a confidence interval for p 1 minus p 2

p1p2 at the given level of confidence.

x 1 equals

x1=357

357, n 1 equals

n1=517

517, x 2 equals

x2=428

428, n 2 equals

n2=589

589, 95

95% confidence

The researchers are

nothing

% confident the difference between the two populationproportions, p 1 minus p 2

p1p2, is between ____and_____?

.

(Use ascending order. Type an integer or decimal rounded to three decimal places asneeded.)

9 The manufacturer of hardness testing equipment usessteel-ball indenters to penetrate metal that is being tested.However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types ofindenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a95% confidence interval to judge whether the two indenters result in different measurements.

Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Specimen 1 2 3 4 5 6 7 8 9

Steel ball 51 57 61 71 68 54 65 51 53

Diamond 53 56 61 74 69 55 68 51 56

Construct a95% confidence interval to judge whether the two indenters result in differentmeasurements, where the differences are computed as'diamond minus steelball'.

The lower bound is ___?

The upper bound is ___?