solve both quactions An engineering consulting firm wanted to evaluate the diame

Question

solve both quactions

An engineering consulting firm wanted to evaluate the diameter of rivet heads. The following data represent the diameters (in hundredths of an inch) for a random sample of 25 rivet heads: 6.81 6.79 6.69 6.59 6.65 6.60 6.74 6.70 6.76 6.84 6.81 6.71 6.66 6.76 6.76 6.77 6.72 6.68 6.71 6.79 6.72 6.72 6.72 6.79 6.83 RIVET (a) Set up a 95% confidence interval estimate of the average diameter of rivet heads (in hundredths of an inch). (b) What assumption must be made in (a)? On the basis of these data, do you think that this assump- tion is valid? Explain. 8.9 The quality engineer of a multinational company involved in manufacturing synthetic rubber wants to examine the hardness of the rubber. In the rubber industry, hardness is measured in degrees Shore. A random sample of 50 pieces of rubber was evaluated, with the following results 62.4 66.0 67.6 63.2 66.3 61.8 61.8 67.5 61.3 65.0 64.6 61.3 64.7 63.5 66.4 60.0 65.8 64.3 62.3 61.4 63.6 69.5 64.9 62.2 67.7 67.7 66.6 64.5 64.0 61.6 68.5 65.2 66.9 66.5 68.3 64.3 63.3 63.6 65.8 60.1 62.6 66.4 67.2 62.5 63.6 63.4 63.1 62.5 68.7 62.2 RUBBER2 (a) Set up a 95% confidence interval estimate of the average hardness (in degrees Shore) for all pieces of rubber of this type. (b) What assumption must be made in (a)? On the basis of these data, do you think that this assump- tion is valid? Explain.

Explanation / Answer

8.8 )

We have givn sample of siz 25 , and we have to find confidence interval for average .

We can use TI84 for finding the confidence interval .

First we have to plug given data in TI84 in list L1 .

Click on STAT --- > select Edit and hit ENTER .

Plug givn data value on by one .

Then for finding confidence interval , click on STAT --- Scroll to th right and selct TESTS and hit ENTER

Scroll down and select T interval and hit ENTER .

Select Input as DATA

List : L1

Freq : 1

C -level : 0.95

Select calculate and hit ENTER

It gives 95%confidence interval as : ( 6.71,6.76 )

From this confidence interval we can suggest that average of data values 95% lies in (6.71 , 6.76 )

8.9 )

In this qustion we have given 50 data values , plug all data values in L1

Again click on STAT --- Scroll to the right and select TESTS

Scroll down and select T Interval and hit ENTER .

Select Input : DATA

List : L1

Freq : 1

C - Level : 0.95

Select calcualt and hit ENTER .

It gives confidence interval as ( 58.73,65.36)

So we can suggest that avrage of given data set 95% lies in interval ( 58.73, 65.36 )

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