An inspection laboratory samples two large shipments of dowel pins by measuring

Question

An inspection laboratory samples two large shipments of dowel pins by measuring both length and diameter. For shipment A, the sample size is 40. the mean diameter is 6.13 mm with a standard deviation of 0.022 mm. and the mean length is 25.4 mm with a standard deviation of 0.140 mm. For shipment B, the sample size is 60. the mean diameter is 6.06 mm with a standard deviation of 0.034 mm. and the mean length is 25.0 mm with a standard deviation of 0.203 mm. Are the two shipments of dowel pins the same? What is the level of confidence in your prediction? Would it be safe to mix the two shipments of pins? Explain.

Explanation / Answer

t test is used to compare mean diameter and mean length of the two shipment A and B.

comparison of mean diameter.

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

40

Sample Mean

6.13

Sample Standard Deviation

0.022

Population 2 Sample

Sample Size

60

Sample Mean

6.06

Sample Standard Deviation

0.034

Intermediate Calculations

Population 1 Sample Degrees of Freedom

39

Population 2 Sample Degrees of Freedom

59

Total Degrees of Freedom

98

Pooled Variance

0.0009

Standard Error

0.0061

Difference in Sample Means

0.0700

t Test Statistic

11.5042

Two-Tail Test

Lower Critical Value

-1.9845

Upper Critical Value

1.9845

p-Value

0.0000

Reject the null hypothesis

comparison of mean length.

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

40

Sample Mean

25.4

Sample Standard Deviation

0.14

Population 2 Sample

Sample Size

60

Sample Mean

25

Sample Standard Deviation

0.203

Intermediate Calculations

Population 1 Sample Degrees of Freedom

39

Population 2 Sample Degrees of Freedom

59

Total Degrees of Freedom

98

Pooled Variance

0.0326

Standard Error

0.0369

Difference in Sample Means

0.4000

t Test Statistic

10.8516

Two-Tail Test

Lower Critical Value

-1.9845

Upper Critical Value

1.9845

p-Value

0.0000

Reject the null hypothesis

For comparing the diameter, t=11.50,P=0.0000, the null hypothesis is rejected and there is significant difference between the two shipments.

For comparing the length, t=10.85,P=0.0000, the null hypothesis is rejected and there is significant difference between the two shipments.

We conclude the two shipments of dowel pins are not same.

b). 0.05 level of confidence is used.

c).

Since there is significant difference in length and diameter, it is not safe to mix.

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

40

Sample Mean

6.13

Sample Standard Deviation

0.022

Population 2 Sample

Sample Size

60

Sample Mean

6.06

Sample Standard Deviation

0.034

Intermediate Calculations

Population 1 Sample Degrees of Freedom

39

Population 2 Sample Degrees of Freedom

59

Total Degrees of Freedom

98

Pooled Variance

0.0009

Standard Error

0.0061

Difference in Sample Means

0.0700

t Test Statistic

11.5042

Two-Tail Test

Lower Critical Value

-1.9845

Upper Critical Value

1.9845

p-Value

0.0000

Reject the null hypothesis

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