Question

Needles! Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a “problem” is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm.

1. Identify the variable of interest and whether the variable is categorical or quantitative.

2. Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers.

a. n= 35, x-bar= 1.64, σ=0.07

b. n=35, μ=1.64, s=0.07

c. n=35, μ=1.64, σ=0.07

d. n=35, x-bar= 1.64, s=0.07

Answer 1

Suppose that a “problem” is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm.

1. Write the appropriate hypotheses using appropriate symbols to test whether the average diameter of needles from the manufacturing process is different from the desired value

Answer :- b. H0: μ= 1.65 mm Ha: μ ≠ 1.65 mm

Because, there are 3 types of symbol used in alternative hypothesis

1) Less than alternative hypothesis used symbol

2) Greater than alternative hypothesis used symbol  

3) Not equal to (diffrent from parameter) alternative hypothesis used symbol  

2. Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers.

Answer :- d. n=35, x-bar= 1.64, s=0.07

Because, here the sample size = n = 35 using this sample we find an average diameter = x-bar = 1.64

and sample standard deviation = s = 0.07

Summary :-

1. Write the appropriate hypotheses using appropriate symbols to test whether the average diameter of needles from the manufacturing process is different from the desired value.

Answer :- b. H0: μ= 1.65 mm Ha: μ ≠ 1.65 mm

2. Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers.

Answer :- d. n=35, x-bar= 1.64, s=0.07