Hamilton Seavey and Stucker measured resistances diameters a

Hamilton, Seavey, and Stucker measured resistances, diameters, and lengths for seven copper wires at two different temperatures and used these to compute experimental resistivities for copper at these two temperatures. Their data follow. The units are 10-8 Ohm-meters.

(a) Suppose that primary interest here centers on the difference between resistivities at the two different temperatures. Assuming normality, give a 90% two-sided confidence interval for the mean difference in resistivity measurements for copper wire of this type at 21.8 degrees C and 0.0 degrees C. (Use 21.8 degrees - 0.0 degrees.) Use at least 3 decimal places in your calculations.

Two-sided confidence interval: [_________ ,__________ ] ohm-meters.

Wire	0.0 degrees C	21.8 degrees C
1	1.52	1.72
2	1.44	1.56
3	1.52	1.68
4	1.52	1.64
5	1.56	1.69
6	1.49	1.71
7	1.56	1.72

Solution

Hamilton, Seavey, and Stucker measured resistances, diameters, and lengths for seven copper wires at two different temperatures and used these to compute experimental resistivities for copper at these two temperatures. Their data follow. The units are 10-8 Ohm-meters.

(a) Suppose that primary interest here centers on the difference between resistivities at the two different temperatures. Assuming normality, give a 90% two-sided confidence interval for the mean difference in resistivity measurements for copper wire of this type at 21.8 degrees C and 0.0 degrees C. (Use 21.8 degrees - 0.0 degrees.) Use at least 3 decimal places in your calculations.

Two-sided confidence interval: [_________ ,__________ ] ohm-meters.

Wire

0.0 degrees C

21.8 degrees C

difference

1

1.52

1.72

0.2

2

1.44

1.56

0.12

3

1.52

1.68

0.16

4

1.52

1.64

0.12

5

1.56

1.69

0.13

6

1.49

1.71

0.22

7

1.56

1.72

0.16

Descriptive statistics

difference

count

7

mean

0.1586

sample standard deviation

0.0393

t table value with 6 Df at 90% level = 1.9432

90% CI = 0.1586 ± 1.9432*0.0393/sqrt(7)

= ( 0.1297, 0.1875)

90% CI = (0.1297, 0.1875) ( 4 decimals)

Wire	0.0 degrees C	21.8 degrees C	difference
1	1.52	1.72	0.2
2	1.44	1.56	0.12
3	1.52	1.68	0.16
4	1.52	1.64	0.12
5	1.56	1.69	0.13
6	1.49	1.71	0.22
7	1.56	1.72	0.16