Question

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 sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected.

a. Define the parameter of interest in the context of this study and assign an appropriate symbol to it.
b. State the appropriate null and alternative hypotheses using the symbol defined in (a).
c. Describe what a Type I error would be in this study. Also, describe the consequence of such an error in the context of this study.
d. Describe what a Type II error would be in this study. Also, describe the consequence of such an error in the context of this study. tudy. Jesti- g so, h the in.

Answer 1

a

True mean diameter
`[\mu]`

b

The null hypothesis is
`H_o : \mu = 1.65 \ mm`

The alternative hypothesis is
`H_a : \mu \\e 1.65`

c

Gnerally type I error occurs when the null hypothesis is wrongfully rejected

The consequence of this is that the wrongfully rejecting a batch of needles because the company do not find strong evidence that its true mean diameter is 1.65 mm whereas it is

d

Gnerally type II error occurs when the null hypothesis is wrongfully accepted

The consequence of this is that the wrongfully accepting a batch of needles because the company do find strong evidence that its true mean diameter is 1.65 mm whereas it is not

Explanation:

Generally from the question we are told that

The needle needs to have a diameter of 1.65 mm

Now statistically the parameter of interest in the context of this study is the true mean diameter of the needle and the symbol is
`\mu`

The null hypothesis is
`H_o : \mu = 1.65 \ mm`

The alternative hypothesis is
`H_a : \mu \\e 1.65`

Gnerally type I error occurs when the null hypothesis is wrongfully rejected

The consequence of this is that the wrongfully rejecting a batch of needles because the company do not find strong evidence that its true mean is 1.65 mm whereas it is

Gnerally type II error occurs when the null hypothesis is wrongfully accepted

The consequence of this is that the wrongfully accepting a batch of needles because the company do find strong evidence that its true mean is 1.65 mm whereas it is not