Question

Give an example of a problem where it would be appropriate to use a statistical hypothesis test for the population mean. Explain what you can determine with such test and how confident you are in your conclusion.

Note : Question is related to lean six sigma

Answer 1

(1)

Example of a problem where it would be appropriate to use a statistical hypothesis test for the population mean :

Suppose a bulb manufacturer wants to estimate the average life of the bulbs procuded by his factory.

For this purpose, the following steps are to to be carried:

Step 1:

Obtain the Sample Size (n) to be selected from the total population usng statistical methods.

Step 2:

From the sample of bulbs obtained, conduct life test on each of the bulb selected and collected dara on life of each bulb selected.

Step 3:

From the data thus collected,calculate the following statistics:

= Sample mean

s = Sample Standard Deviation.

For the given example,let the values be:

n = Sample Size = 20

= Sample mean = 1500 hours

s = Sample Standard Deviation = 120 hours

Selecte Signifince Level = = 0.05

Step 4:

Degrees of freedom = n -1 = 20 - 1 = 19

From Table, critical values of t = 2.093

Step 5:

95% Confidence interval for average life of bulbs:

(2)

Question:

Explain what you can determine with such test

Using the above procedure the manufacturer can determine the average life of the bulbs produced by him.

(3)

Question:

How confident you are in your conclusion.

The 95% confidence interval (1443.838, 1556.162) is a rrrange of values the manufacturer is 95% confident will contain true unknown average life of bulbs produced by him.