P-value Calculation for Water Filter Defect Experiment

[schapman22]

Homework Statement

A manufacturing company produces water filters for home refrigerators. The process has typically produced about 4% defective. A recently designed experiment has led to changing the seal to reduce defects. With the process running using the new seal, a random sample of 300 filters yielded 7 defects.

Homework Equations

H₀: null hypothesis
H₁: alternative hypothesis

The Attempt at a Solution

H₀: p not equal to 7/300?
H₁: p=7/300?

I have looked up examples of null hypothesis but I am not sure how to apply it to this problem.

 

[Mark44]

Homework Statement

A manufacturing company produces water filters for home refrigerators. The process has typically produced about 4% defective. A recently designed experiment has led to changing the seal to reduce defects. With the process running using the new seal, a random sample of 300 filters yielded 7 defects.

Homework Equations

H₀: null hypothesis
H₁: alternative hypothesis

The Attempt at a Solution

H₀: p not equal to 7/300?
H₁: p=7/300?

I have looked up examples of null hypothesis but I am not sure how to apply it to this problem.

The null hypothesis should involve the population statistic, not the observed sample statistic.

So your null hypothesis should be H₀: p = .04

Can you infer from the problem statement what the alternate hypothesis should be?

 

[schapman22]

would it be H₁: p ≠ .04?

 

[Mark44]

No.
What does this suggest to you?

The process has typically produced about 4% defective. A recently designed experiment has led to changing the seal to reduce defects.

 

[schapman22]

H1: p < .04?

 

[Mark44]

Yes. In ordinary language, the null hypothesis is: The new seal makes no difference. The alternate hypothesis is: The new seal reduces the defect rate.

 

[schapman22]

Okay, I got that the test statistic is -1.5 by doing Z=(.023-.04)/sqrt(.04*.96/300) is this correct? And how would I find the critical value at a .05 level of significance? By the way thank you so much for all the help.

 

[Mark44]

What you got looks OK to me.

To find the critical value, look in a table of the standard normal distribution for the number in the table that is closest to 0.9500, and read off the z value for that probability. What this is telling you is P(Z < something) = .9500. That "something" will be a positive value. What you want for your critical value is -<something>, the value such that P(Z < -(something)) = .0500.

It helps to draw a sketch of the standard normal (Z) distribution, and recognize that it has symmetry across the vertical axis.

 

[schapman22]

Okay my table has Z_.005=1.645 so I would use -1.645 for my critical value I believe? and the final part of this question which I am unsure about it is I need the p value which I know is the probability of getting the sample results.

 

[Mark44]

Okay my table has Z_.005=1.645

Before, you said at the .05 level. Is the above a typo or did you look at the wrong value?

so I would use -1.645 for my critical value I believe? and the final part of this question which I am unsure about it is I need the p value which I know is the probability of getting the sample results.

 

[schapman22]

yes sorry I meant .05 not .005

 

[Mark44]

I corrected the .005 that you had.

Okay my table has Z_.05=1.645 so I would use -1.645 for my critical value I believe?

Yes.
So if Z < -1.645, you would accept the alternate hypothesis.

In your earlier calculation, you got Z = -1.5.

and the final part of this question which I am unsure about it is I need the p value which I know is the probability of getting the sample results.