ChiSquare vs. z Section 25.9


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1 ChiSquare vs. z Section 25.9 Lecture 49 Robb T. Koether HampdenSydney College Wed, Apr 20, 2016 Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
2 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
3 Example There are two situations where the χ 2 test has 1 degree of freedom. A goodnessoffit test with only 2 categories. A twoway table with 2 rows and 2 columns. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
4 Example There are two situations where the χ 2 test has 1 degree of freedom. A goodnessoffit test with only 2 categories. A twoway table with 2 rows and 2 columns. In these cases, the test could be performed as a ztest. Goodnessoffit test Test of one proportion. 2 2 table Comparing two proportions. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
5 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
6 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
7 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
8 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: The sample proportion is ˆp = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
9 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: The sample proportion is ˆp = The test statistic is z = (0.5)(0.5) 1000 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
10 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
11 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: The observed and expected counts: Heads Tails Total Obs Exp Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
12 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: The observed and expected counts: The test statistic is Heads Tails Total Obs Exp χ 2 = ( ) ( )2 500 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
13 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
14 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
15 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
16 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
17 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
18 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = The pooled estimate is ˆp = = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
19 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = The pooled estimate is ˆp = = = The test statistic is z = (0.575)( ) ( ) = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
20 2 2 Table Using the goodnessoffit test: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
21 2 2 Table Using the goodnessoffit test: The 2 2 table is Heads Tails Total Coin Coin Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
22 2 2 Table Using the goodnessoffit test: The 2 2 table is Heads Tails Total Coin Coin Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
23 2 2 Table Using the goodnessoffit test: The 2 2 table is The test statistic is Heads Tails Total Coin Coin χ 2 = ( ) ( ) ( ) ( )2 425 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
24 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
25 Assignment Assignment Read Sections Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
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