Complete Question
A machining process produces screws for which the population proportion of screws with defective threads is .10 (10%). A new laser-enhanced process has become available and the developer claims that the population proportion of screws with defective threads will be less than .10. To test the validity of this claim, 900 screws produced by the new process are selected at random and the sample proportion of defectives is computed. This result will be used to make a decision as to whether or not the manufacturer should invest in the new process.
7) Which of the following should be used as the alternative hypothesis?
A) p = 0.10 B) [tex]p \ne 0. 10[/tex] C) [tex]p \le 0.10[/tex] D) p > 0.10 E) p < 0.10
8) Determine the p-value of the test statistic if [tex]\r p= 0.076[/tex] (Round your answer to 4 decimal places.)
A) .9836 B) .0082 C) -.0082 D) .0164 E) .9918
Answer:
7
The correct option is E
8
The correct option is B
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The claim : the population proportion of screws with defective threads will be less than [tex]p = 0.10[/tex]
The sample size is n = 900 screws
The null hypothesis is
[tex]H_o : p = 0.10[/tex]
The alternative hypothesis is
[tex]H_a : p < 0.10[/tex]
Generally the reason why the above statement is the alternative hypothesis is because the statement for the null hypothesis must have an equality sign present, hence the alternative hypothesis then represents the claim
Generally the test statistics is mathematically represented as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p ( 1- p )}{n} } }[/tex]
=> [tex]t = \frac{0.076 - 0.10 }{ \sqrt{ \frac{0.10 ( 1- 0.10 )}{900} } }[/tex]
=> [tex]t = -2.4[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(t < -2.4)[/tex]
From the z-table
[tex]P(t < -2.4) = 0.0082[/tex]
