A sample of the package times in seconds of two machines is

A sample of the package times (in seconds) of two machines is provided below. You wish to determine if there is evidence that the two machines have the same variability in the package times. What is the correct statement of hypothesis for this tes

Old Machine [B]

New Machine [A]

42.70

42.10

43.80

41.30

42.50

42.40

43.10

43.20

44.00

41.80

43.60

41.00

43.30

41.80

43.50

42.80

41.70

42.30

44.10

42.70

²_A ²_B;   H₁: ²_A < ²_B

H₀:           _A = _B;   H₁:          _{A B}

H₀:   ²_A = ²_B;   H₁:       ²_A ²_B

H₀: P_A = P_B;   H₁:          P_A P_B

H₀:   _D = 0;   H₁:            _D 0

None of the above

What is the value of the t-statistic associated with this test?

Old Machine [B]	New Machine [A]
42.70	42.10
43.80	41.30
42.50	42.40
43.10	43.20
44.00	41.80
43.60	41.00
43.30	41.80
43.50	42.80
41.70	42.30
44.10	42.70

Solution

A sample of the package times (in seconds) of two machines is provided below. You wish to determine if there is evidence that the two machines have the same variability in the package times. What is the correct statement of hypothesis for this tes

Old Machine [B]

New Machine [A]

42.70

42.10

43.80

41.30

42.50

42.40

43.10

43.20

44.00

41.80

43.60

41.00

43.30

41.80

43.50

42.80

41.70

42.30

44.10

42.70

²_A ²_B;   H₁: ²_A < ²_B

H₀:           _A = _B;   H₁:          _{A B}

H₀:   ²_A = ²_B;   H₁:       ²_A ²_B

H₀: P_A = P_B;   H₁:          P_A P_B

H₀:   _D = 0;   H₁:            _D 0

None of the above

We want to to determine if there is evidence that the two machines have the same variability in the package times.

So correct hypothesis is H₀:   ²_A = ²_B;   H₁:       ²_A ²_B

What is the value of the t-statistic associated with this test?

F test is the appropriate test F=1.2039

F Test for Differences in Two Variances

Data

Level of Significance

0.05

Larger-Variance Sample

Sample Size

10

Sample Variance

0.562333333

Smaller-Variance Sample

Sample Size

10

Sample Variance

0.467111111

Intermediate Calculations

F Test Statistic

1.2039

Population 1 Sample Degrees of Freedom

9

Population 2 Sample Degrees of Freedom

9

Two-Tail Test

Upper Critical Value

4.0260

p-Value

0.7868

Do not reject the null hypothesis

Old Machine [B]	New Machine [A]
42.70	42.10
43.80	41.30
42.50	42.40
43.10	43.20
44.00	41.80
43.60	41.00
43.30	41.80
43.50	42.80
41.70	42.30
44.10	42.70