An aircraft manufacturer needs to buy aluminum sheets with an average thickness

Question

An aircraft manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inch. The manufacturer knows that significantly thinner sheets would be unsafe and considerably thicker sheets would be too heavy. A random sample of 100 sheets from a potential supplier is collected.

a. Use the p-value approach to determine if the aircraft manufacturer should buy aluminum sheets from the supplier.

b. For which values of the sample mean would the aircraft manufacturer decide to buy sheets from this supplier, assuming = 0.05?

Please, show your work.

Sheet Thickness 1 0.0403 2 0.0693 3 0.0632 4 0.0651 5 0.0534 6 0.0574 7 0.0400 8 0.0515 9 0.0542 10 0.0555 11 0.0512 12 0.0525 13 0.0434 14 0.0392 15 0.0607 16 0.0575 17 0.0637 18 0.0358 19 0.0455 20 0.0319 21 0.0578 22 0.0488 23 0.0402 24 0.0318 25 0.0447 26 0.0306 27 0.0325 28 0.0542 29 0.0416 30 0.0517 31 0.0448 32 0.0520 33 0.0495 34 0.0525 35 0.0618 36 0.0571 37 0.0391 38 0.0655 39 0.0568 40 0.0370 41 0.0505 42 0.0425 43 0.0611 44 0.0491 45 0.0574 46 0.0603 47 0.0420 48 0.0616 49 0.0463 50 0.0340 51 0.0609 52 0.0457 53 0.0409 54 0.0367 55 0.0713 56 0.0576 57 0.0515 58 0.0549 59 0.0325 60 0.0470 61 0.0203 62 0.0379 63 0.0442 64 0.0384 65 0.0409 66 0.0358 67 0.0442 68 0.0538 69 0.0486 70 0.0317 71 0.0529 72 0.0449 73 0.0437 74 0.0384 75 0.0400 76 0.0397 77 0.0486 78 0.0296 79 0.0548 80 0.0407 81 0.0552 82 0.0412 83 0.0425 84 0.0371 85 0.0590 86 0.0398 87 0.0600 88 0.0589 89 0.0496 90 0.0509 91 0.0427 92 0.0481 93 0.0512 94 0.0504 95 0.0467 96 0.0253 97 0.0195 98 0.0471 99 0.0464 100 0.0529

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   0.05  
Ha:    u   =/   0.05  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    0.047387          
uo = hypothesized mean =    0.05          
n = sample size =    100          
s = standard deviation =    0.010430682          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.5051095          
              
Also, the p value is              
              
p =    0.012241349   [P VALUE]      
  
              
As P is small, say P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that the average thickness is not 0.05 in, and the aircraft manufacturer should not buy aluminum sheets from the supplier. [CONCLUSION]

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b)

Hence, we construct a 1-0.05 = 0.95 confidence interval.

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    0.05          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    0.010430682          
n = sample size =    100          
              
Thus,              
Margin of Error E =    0.002044376          
Lower bound =    0.047955624          
Upper bound =    0.052044376          
              
Thus, the confidence interval is              
              
(   0.047955624   ,   0.052044376   ) [ANSWER]

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