Exercise Quiz 10

Plastic screens for a production of a specific lamp is planned to be outsourced to a subcontractor. It is essential for the lamp’s density, that the plastic screens have the correct dimensions. Two subcontractors are contacted.

From subcontractor A, 500 items are received: out of these, there are 4 that do not comply with the requirements for the dimensions.

From subcontractor B, 700 items are received: out of these, there are 8 that do not comply with the requirements for the dimensions.

The following hypothesis test is to be carried out:

\[\begin{array}{l} {H_0}:p_A=p_B \\ {H_1}:p_A\not= p_B \end{array}\]

The P-value and the conclusion for this test is:

P-value=0.56. $ H_0 $ can be rejected at level 5%.

P-value=0.56. $ H_0 $ cannot be rejected at commonly used significance levels.

P-value=12/1200=0.01. $ H_0 $ can be rejected at level 5%.

P-value=0.28. $ H_0 $ can be rejected at commonly used significance levels.

P-value=0.001. $ H_0 $ cannot be rejected at commonly used significance levels.

A company that sells outdoor lighting has a lamp made in 3 material variations: in copper, with a painted surface and stainless steel. The lamps are sold in Denmark and exported mainly to the Netherlands and Norway. For 250 Lamps the relative distribution of sales between the 3 variants and 3 different countries were recorded The data is shown in the following table:

Variants	Denmark	the Netherlands	Norway
Cobber	7.2%	5.2%	1.2%
Painted	28.0%	14.0%	20.8%
Stainless	8.8%	4.8%	10.0%

The following testing is wanted: $H_0: \mbox{ Independence between variant and country}$ $H_1: \mbox{ Dependence}$ using the for this situation suitable test.

What is the expected number of lamps for the material copper sold in Denmark, assuming thet $ H_0 $ is true:

$e_{11}=18$

$e_{11}=\frac{34\cdot 110}{250}=14.96$

$e_{11}=\frac{250}{110}=2.27$

$e_{11}=\frac{250}{34}=7.35$

$e_{11}=\frac{18\cdot 110}{250}=7.92$

If you did the previous exercise, the following is a repetition:

A company that sells outdoor lighting has a lamp made in 3 material variations: in copper, with a painted surface and stainless steel. The lamps are sold in Denmark and exported mainly to the Netherlands and Norway. For 250 Lamps the relative distribution of sales between the 3 variants and 3 different countries were recorded The data is shown in the following table:

Variants	Denmark	the Netherlands	Norway
Cobber	7.2%	5.2%	1.2%
Painted	28.0%	14.0%	20.8%
Stainless	8.8%	4.8%	10.0%

The following testing is wanted: $H_0: \mbox{ Independence between variant and country}$ $H_1: \mbox{ Dependence}$ using the for this situation suitable test.

The critical value for the appropriate test on level 1% is:

9.488

1.96

3.841

7.789

13.277

02323 · Exercise Quiz 10

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