Meme for single samp from a s Point value is sampled that ly has a these a n one

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Meme for single samp from a s Point value is sampled that ly has a these a n one setting known interval for can be Summary from a normal population with m LerX be single value sampled level 1000I-a) e is known then a Exercises for Section 5.4 Finda9ss confidence interval 1. Find the value of needed to level with the sided confidence interval of the given 6 Achemist made eight independent meawurrar the melting point of tungstea Sho oburied a Level90s, sample 9. mean el 3410.14 c and a sample standard deia b Level 9ss, ample sine 5. Level 99s, ample sine 29. a use the student's r distribution lo a Level 9%, sample size 2 confidence interval for the melting p 2 Fnd the value of needed construct an upper or lower confidence bound in each ofthe siaations Use the student's r distribution to find a confidence interval for the melting pois Find the level of a two ided confdenceintenal that If the eight measurements had been is based on the given value of t and the given 3409.80, 3412.66, 0979, 2409.76, 3aNT, 3409,80, 3409,78, would the confidence interi a, r 2179, sample above be valid? Explain. br-3365 sample sine 6. 7. Eight independent measurements are taken d 4-32007 sample size ameter of a piston. The measurements 3236.3223.3242 3.244.3.228, 3.253,325A3 3701 sample sine 27. Make a dxplot ofthe eight values. 4 Five measurements are taien of the octane rating for particular pe of gasoline The results in s) are 870, 865. 8.0 85.3 Fiad 99 inneral for the mean octane rating for ais type Should the Student's r distribution be edtofl a 99% confidence interval for the diameserefta piston? If so, find the confidence interval plain why not. s, Amodelelheat transfer from acylinder immersed in liquid predicts that the heat transfer ooeffairn for the diameter of another piston ne measuremeno ginder will become contant al very lew fou time are 3.295, 3,232.326I, 324g,32s9,3 of the fluid. A sample of IO 1576.3.201. Make dotplot ofthese values The results, in Whm K, are d should de student's distributienbe edvl a 95% 37 confidence interval for the diameter 14.1 144 12.2 119 11.8 piston? If so, find the coefdence interval O O O

Explanation / Answer

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SOLUTION1A:

Two-sided gives the two-sided significance level

Find a critical value for a 90% confidence level.

Step 1: Subtract the confidence level from 100% to find the level: 100% – 90% = 10%.

Step 2: Convert Step 1 to a decimal: 10% = 0.10.

Step 3: Divide Step 2 by 2 (this is called “/2”).
0.10 = 0.05. This is the area in each tail.

Step 4: Subtract Step 3 from 1 (because we want the area in the middle, not the area in the tail):
1 – 0.05 = .95.

Step 5: Look up the area from Step in the T-table

For n-1 =9-1=8 df and 0.95 level of significance is +-2.306

Solution1b:

alpha=1-0.95=0.05

alpha/2=0.025

1-alpha/2=1-0.025=0.975

df=5-1=4

t critica=+-3.495

Solution1c:

alpha=1-0.99=0.01

alpha/2=0.01/2=0.005

df=n-1=29-1=28

Solution1d:

alpha=1-0.95=0.05

alpha/2=0.05/2=0.025

df=n-1=2-1=1

t-value (two-tailed): +/- 3.04692878

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