Question

Assembly Times
114.2
111.4
119.2
122.2
133.3
125.6
123.6
116.3
112.7
112.5
119.9
114.0
119.0
117.0
128.2
110.5
120.5
120.8
118.4
109.5
108.9
116.6
127.0
123.6
115.1
114.1
129.4
122.8
110.5
119.9
116.9
122.4
110.7
121.3
121.9
113.7
126.0
123.1
114.8
116.6
118.8
119.0
121.5
113.0
109.5
122.0
117.5
115.0
127.9
122.1
Assembly Times
114.2
111.4
119.2
122.2
133.3
125.6
123.6
116.3
112.7
112.5
119.9
114.0
119.0
117.0
128.2
110.5
120.5
120.8
118.4
109.5
108.9
116.6
127.0
123.6
115.1
114.1
129.4
122.8
110.5
119.9
116.9
122.4
110.7
121.3
121.9
113.7
126.0
123.1
114.8
116.6
118.8
119.0
121.5
113.0
109.5
122.0
117.5
115.0
127.9
122.1

An automotive assembly department conducts a study on the time required to complete a specific assembly task. Fifty (50) cycles of the assembly process were completed and the assembly times (in seconds) were recorded. The data are provided in this data file. Analyze the data to answer the quiz questions.

The margin of error associated with the point estimate in problem 1

A 95% confidence interval for the mean is given by?

The correct interpretation for the confidence interval in problem 3 is:

	1.	The true mean, μ, will fall within the given interval 95% of the time.
	2.	The confidence interval bounds the true mean, μ, with probability 0.95.
	3.	The sample mean will fall with the given interval 95% of the time.
	4.	The confidence interval bounds the sample mean with probability 0.95.

	1.	(117.03, 120.19)
	2.	(115.02, 122.31)
	3.	(119.56, 125.74)
	4.	(116.98, 120.24)

Answer 1

Mean of the Assembly times, = = 118.608 seconds

Std Deviation of assembly times, = 5.744 seconds

Ans 1) As sample size = 50 (> 30), the mean of sample assembly times follows a normal distribution, with standard deviation = std error of the sample = = 5.744 / = 0.812

95% confidence interval for the mean lies 1.96 std deviation on either side of the sample mean.

Hence 95% confidence interval for the mean = 1.96* = 118.608 1.96*0.812 = (117.03, 120.19) (option 1)

Ans 2)  The confidence interval above means the true mean will lie within this confidence interval 95% of the time. Hence, correct option is Option 1