their data are recorded here. in frequency table are the measurements obt 50 scr

ID: 3360212 • Letter: T

Question

their data are recorded here. in frequency table are the measurements obt 50 screws by one of the students using the Interpret the statement, The interval from 6.3 to Given Dis a 95% confidence interval for the mean On 2. In Chapter Exercise 2 of Chapter 3, there i ata set consisting of the aluminum contents of 26 bihourly samples of recycled PET plasti a recycling facility. Those 26 measurements have y = 1427@m and s ~ 98.2 ppm Sethese facts to respond to the following. (Assume that n26 f large-sample Diameter (mm) Frequency 4.52 4 is large enough to permit the formulas in this case.) (a) Mak 4.67 4.68 4.69 4.70 4.71 e a 90% two-si idence interval for the mean aluminum content of such specimens 14 over the 52-hour penod (b) Make a 95% tw onfidence interval for the mean aluminum content of such specimens over the 52-hour study period. How does this 4 4 compare to your answer to part (a)? (a) Compute the sample mean and standard devi- (c) Make a 90% upper cor nce bound for the mean aluminum content of such samples over the 52-hou y period # such that (-00,#) 0% confidence interval.) How per endpoint ation for these data. (b) Use your sample values from (a) and make a 98% two-sided confidence interval for the mean diameter of such screws as measured b this student with these calipers does this value compare to of your inter mean aluminum content of such compare to your answer to part (c I from part (a) (c) Repeat part(b) using 99% confidence. How (d) Make a % upper confidenc bound for the samples over the 52-hour study period. How does this value does this intervai compare with the one from (b)? (d) Use your values from (a) and find a 98% lower (e) Interpret your interval from (a) for someone with litle statistical background. (Speak in the context of the recycling study and use Defini confidence bound for the mean diameter. (Find a number # such that (#, oo) is a 98% confi dence interval.) How does this value compare to the lower endpoint of your interval from (b)? tion 2 as your guide.) (e) Repeat (d) using 99% confidence. How does 3. Return to the context of Exercise 2. Supposethat in order to monitor for possible process changes, fu- ture samples of PET will be taken. If it is desirable to estimate the mean aluminum content with +20 ppm precision and 90% confidence, what future the value computed here compare to your an swer to (d)? (f) Interpret your interval from (b) f or someone with little statistical background. (Speak in ti context of the diameter measurement stu use Definition 2 as your guide.) y and ple size do you recommend? 4. DuToit, Hansen, and Osborne measured the diam- eters of some no. 10 machine screws with two dif ferent calipers (digital and vernier scale). Part of

Explanation / Answer

Result:

a).

FREQUENCY

fx.x

4.52

20.4304

4.66

18.64

86.8624

4.67

32.69

152.6623

4.68

32.76

153.3168

4.69

65.66

307.9454

4.7

42.3

198.81

4.71

18.84

88.7364

4.72

18.88

89.1136

Total

234.29

1097.877

Mean=234.29/50=4.69

Sd=sqrt((1097.877-234.29^2/50)/49)

=0.029

b).

Table value t at 50-1 = 49 DF =2.4049

98% CI = ar x pm t* rac {s}{sqrt{n}}

= 4.69 pm 2.4049* rac {0.029}{sqrt{50}}

=(4.6801, 4.6999)

c).

Table value t at 50-1 = 49 DF =2.680

99% CI = ar x pm t* rac {s}{sqrt{n}}

= 4.69 pm 2.680* rac {0.029}{sqrt{50}}

=(4.679, 4.701)

99CI is wider 98% CI.

d).

lower Table value t at 50-1 = 49 DF =-2.11

98% LCI = 4.69 - 2.11* 0.029/sqrt(50)

=4.6813

e).

lower Table value t at 50-1 = 49 DF =-2.405

99% LCI = 4.69 - 2.405* 0.029/sqrt(50)

=4.6801