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Chapter 14: Q8CQQ (page 654)

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

What is the value of\(\bar \bar x\)? In general, how is a value of\(\bar \bar x\)found?

Short Answer

Expert verified

The value of\(\bar \bar x\)is equal to 2.24 feet.

The general formula to compute the value of\(\bar \bar x\)is as follows:

\(\bar \bar x = \frac{{{{\bar x}_1} + {{\bar x}_2} + ... + {{\bar x}_N}}}{N}\)

Here,

\({\bar x_i}\)and N represent the mean of the ith sample and the total number of samples, respectively.

Step by step solution

01

Given information

When aviation altimeters are tested in a pressure chamber, the \(\bar x\)chart is plotted to show the measurement of errors (in feet). The sample size for each individual is 100.

02

Step 2:Value of \(\bar \bar x\)

By observing the\(\bar x\)chart, the value of\(\bar \bar x\)is written on the left side beside the centerline.

Thus, the value of\(\bar \bar x\)is equal to 2.24 feet.

First, calculate the average ( or mean) of each of the subgroups and then obtain the mean of subgroups means.

The general formula to compute the value of\(\bar \bar x\)is as follows:

\(\bar \bar x = \frac{{{{\bar x}_1} + {{\bar x}_2} + ... + {{\bar x}_N}}}{N}\),where

\({\bar x_i}\)is the mean of the ith sample, and

N is the total number of samples.

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Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. (Most of the data are real, but some are fabricated.) Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. Data are available for download atwww.TriolaStats.com.


Jan.-Feb.

Mar.-April

May-June

July-Aug.

Sept.-Oct.

Nov.-dec.

Year 1

3637

2888

2359

3704

3432

2446

Year 2

4463

2482

2762

2288

2423

2483

Year 3

3375

2661

2073

2579

2858

2296

Year 4

2812

2433

2266

3128

3286

2749

Year 5

3427

578

3792

3348

2937

2774

Year 6

4016

3458

3395

4249

4003

3118

Year 7

5261

2946

3063

5081

2919

3360

Year 8

3853

3174

3370

4480

3710

3327

Energy Consumption: Notation After finding the values of the mean and range for each year, find the values of\(\bar \bar x\)and\(\bar R\). Then find the values of LCL and UCL for an R chart and find the values of LCL and UCL for an\(\bar x\)chart.

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