PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Chapter 8.2, Problem 50E

(a)

To determine

To explain how large a sample must you test to estimate the proportion of PTC tasters within 0.04 with 90% confidence.

(a)

Expert Solution
Check Mark

Answer to Problem 50E

  n=318 .

Explanation of Solution

It is given that:

  E=0.04p^=0.75

Now, we know that the formula for sample size is as:

  p^ known: n=[zα/2]2p^q^E2=[zα/2]2p^(1p^)E2p^ unknown: n=[zα/2]20.25E2

For confidence level 1α=0.90 determine zα/2=z0.05 using Table A, the z -score is then,

  zα/2=1.645

Thus, p^ is known, then the sample size is calculated as:

  n=[zα/2]2p^(1p^)E2=1.6452×0.75(10.75)0.042=318

(b)

To determine

To answer the question in part (a) again but this time use the conservative guess p^=0.5 and find out by how much do the two sample sizes differ.

(b)

Expert Solution
Check Mark

Answer to Problem 50E

The sample size increased by 105 .

Explanation of Solution

It is given that:

  E=0.04p^=0.50

From part (a) we have,

  n=318

Now, we know that the formula for sample size is as:

  p^ known: n=[zα/2]2p^q^E2=[zα/2]2p^(1p^)E2p^ unknown: n=[zα/2]20.25E2

For confidence level 1α=0.90 determine zα/2=z0.05 using Table A, the z -score is then,

  zα/2=1.645

Thus, p^ is known, then the sample size is calculated as:

  n=[zα/2]2p^(1p^)E2=1.6452×0.50(10.50)0.042=423

Thus, the difference between the two sizes is as:

  423318=105

Thus, we note that the sample size increased by 105 .

Chapter 8 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.3 - Prob. 76ECh. 8.3 - Prob. 77ECh. 8.3 - Prob. 78ECh. 8.3 - Prob. 79ECh. 8.3 - Prob. 80ECh. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Prob. 83ECh. 8.3 - Prob. 84ECh. 8.3 - Prob. 85ECh. 8.3 - Prob. 86ECh. 8 - Prob. R8.1RECh. 8 - Prob. R8.2RECh. 8 - Prob. R8.3RECh. 8 - Prob. R8.4RECh. 8 - Prob. R8.5RECh. 8 - Prob. R8.6RECh. 8 - Prob. R8.7RECh. 8 - Prob. R8.8RECh. 8 - Prob. R8.9RECh. 8 - Prob. T8.1SPTCh. 8 - Prob. T8.2SPTCh. 8 - Prob. T8.3SPTCh. 8 - Prob. T8.4SPTCh. 8 - Prob. T8.5SPTCh. 8 - Prob. T8.6SPTCh. 8 - Prob. T8.7SPTCh. 8 - Prob. T8.8SPTCh. 8 - Prob. T8.9SPTCh. 8 - Prob. T8.10SPTCh. 8 - Prob. T8.11SPTCh. 8 - Prob. T8.12SPTCh. 8 - Prob. T8.13SPT
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