Unknown to a quality assurance technician the tensile streng

Unknown to a quality assurance technician, the tensile strengths (in pounds per square inch, psi) for all 500 heavy-duty construction bolts in a recent shipment are as listed in file XR04074. Because a bolt must be broken to measure its strength, the testing process is is destructive. The technician plans to collect a simple random sample of 20 bolts, then measure how much tension each one withstands before it breaks. Generate the simple random sample and compute its mean breaking strength. Assuming that the bolt manufacturer has advertised that, on average, such bolts will withstand 10,000 psi, refer to your sample result in commenting on the manufacturer’s claim. (We will discuss the use of sample data in evaluating claims in much greater detail in Chapter 10, Hypothesis Testing.)

Solution

Let the 20 readings of mean be

2.01, 2.02, 2, 1.97, 1.8, 3, 2.5, 2.7, 2.6, 2.5 , 2.4,2.42, 2.91, 1.99, 2.12, 2.30, 2.45, 2.31, 2.21, 2.56

Mean of these 20 =2.3385

Std dev = 0.3182

Std error = std deviation/square root of n = 0.3182/rt 20

=0.0712

As sample size is small, and population std dev not known t test can be used

t statistic = mean diff/std error

Let us assume that mean = 2

H0: mu =2

Ha: mu <2

(Left tailed test)

t = 0.3385/0.3182

=1.064

df = 20-1 =19

p value = 0.150332.

Let us take alpha as 0.05

The result is not significant at p < .05.

Hence accept null hypothesis

and reject the strength is unable to bear not even 2