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. Required:
a. What should be used as the alternative hypothesis?
b. Determine the p-value of the test statistic if p ^ = 0.076.

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) C) D) p > 0.10 E) p < 0.10

8) Determine the p-value of the test statistic if (Round your answer to 4 decimal places.)

A) .9836 B) .0082 C) -.0082 D) .0164 E) .9918

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  

    The  claim :  the population proportion of screws with defective threads will be less than  

    The sample size is  n =  900  screws

The null hypothesis is

The alternative hypothesis is  

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

=>        

=>    

Generally  the p-value is mathematically represented as

From the z-table  

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40