Question

You are a quality control officer for a hair-dryer company. If the percentage of defective hairdryers 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 ?? =.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 1

Part a. Which test would you use and why?

We use here one proportion test.

Here claim is given in percent which is 5% ( p =5% )

n = 157 and x = number of success = 9

Part b. Write the null and alternative hypothesis in complete sentences

Claim : to determine if greater than 5% of the hair dryers are defective.

H0 : equal or less 5% of the hair dryers are defective

Ha:   greater than 5% of the hair dryers are defective.

Part c. Write the null and alternative hypothesis as symbols.

Hypothesis :

Part d.

np = 157*0.05 = 7.85

n*(1-p) = 157*(1-0.05) = 149.15

both np and n(1-p) are greater than 5 therefore we can use normal distribution or Z test for proportion

Part e

Test Statistics

Z = 0.42

P value : 0.3372    ( Using Z table check 0.4 row and 0.02 column we get 0.6628 which is left side region we have > sign in Ha hence subtract this value from 1 )

Decision :

? =.05

P value > 0.05 hence we fails to reject null.

Conclusion :

There is not sufficient evidence to conclude that greater than 5% of the hair dryers are defective.

Using decision we can say Equal or less than 5% of the hair dryers are defective.