A production line produces rulers that are supposed to be 12 inches long. A sample of 49 of the rulers had a mean of 12.1 and a standard deviation of .5 inches. The quality control specialist responsible for the production line decides to do a hypothesis test at the 90 percent significance level to determine whether the production line is really producing rulers that are 12 inches long or not. a. What is the null hypothesis? b. What is the alternative hypothesis? c. What is the value of the test statistic? d. What is the rejection region (with its numerical value)? e. What conclusion do you draw? f. What does this mean in terms of the problem situation?

a) Null hypothesis:  

b) Alternative hypothesis:  

c)  

d)

And the rejection region would be

e) Since the calculated value is not on the rejection zone we can't reject the null hypothesis

f)For this case we can conclude at 10% of significance that the true mean is not significantly different from 12 and then the specification is not violated.

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the sample deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

Part a

We need to conduct a hypothesis in order to check if the mean is equal to 12 or not, the system of hypothesis would be:  

Null hypothesis:  

Part b

Alternative hypothesis:  

Part c

The statistic is given by:

(1)  

Part d

For this case since we are conducting a bilateral test we need to find the degrees of freedom first given by:

And we need to find a critical value in the distribution with 48 degrees of freedom who accumulates of the area and we got:

And the rejection region would be

Part e

Since the calculated value is not on the rejection zone we can't reject the null hypothesis

Part f

For this case we can conclude at 10% of significance that the true mean is not significantly different from 12 and then the specification is not violated.

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

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step-by-step explanation:

step-by-step explanation:

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