Question 1162495: 4. You are a quality control officer for a hair-dryer company. If the percentage of defective hair- dryers that you test is statistically greater than 5%, then you have to get rid of the batch. You collect a simple random sample of 157 hair dryers and find that 9 of them are defective. Conduct a hypothesis test with a 𝛼𝛼 =.05 level of significance to determine if greater than 5% of the hair dryers are defective. Write all non-calculation answers in complete sentences.
a. Which test would you use and why?
b. Write the null and alternative hypothesis in complete sentences. (Make sure you mark
which is the null and which is the alternative.)
c. Write the null and alternative hypothesis as symbols.
d. State the requirements that have been met to run the test.
e. What is the test statistic and the p-value? (Make sure you use the right notation.)
f. Should you reject or fail to reject the null hypothesis?
g. State the conclusion for the test.
h. According to the results of your hypothesis test, should you get rid of the batch. Explain
your reasoning based upon the hypothesis test
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use a 1 sample proportion test because you are testing a proportion greater or less than 5%
Ho: the true proportion is <=5%
Ha: the proportion is> 5%
alpha is 0.05 p{reject Ho|Ho true}
test statistic is a z
reject if z >1.645
SRS was done, and np and n(1-p) are both >5
z=(p hat -0.05)/sqrt(p(1-p)/n)
p hat=0.0573
z=0.0073/0.0173
z=0.42
p-value is 0.34
fail to reject Ho, since z < the critical value of 1.645
There is insufficient evidence based on this sample to conclusively state at the 5% interval that the batch is defective. If the true proportion were 5% we would have a 34% chance of having a result this much or more from the mean.
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