# Chapter 1. The Sample Proportion $$\widehat{p}$$

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Stat Tutor
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true

2:06

### Question 1.1

LEhi27LQa58LKxhEgZs7pswhec22J+wmTjwXUr02lJMfZ6A/1P0qm2kONM55v7KyKdkqwVahXJSkJx91g6uvgbEGTlexMYuVPoPc3ifJLEDSc43kleYctOcG0daxZhjX
Incorrect. We compute proportion when the response variable is categorical.
Correct. We compute proportion when the response variable is categorical.
Incorrect. Try again.
2

### Question 1.2

+vev1Z6hIieqW/W6S/DKQxwYmXE1aszoPG6okR47oxzW3Djlh3FBlV5Wgcqeg3Hx3oN9PJOasTKT8ezBe4sltQuUiRMLcOFuD8XOXnc0E6lwvbu6r1naF0jbJ+M1DSh0Tropxgn7EZTcSsX7lLfU0b+swUI=
Incorrect. "p" is the symbol for population proportion.
Correct. "p" is the symbol for population proportion.
Incorrect. Try again.
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3:52

### Question 1.3

wuXGE6AYLFjCAIu9Wh2e3mn1G8eqoFF3fyrH4mShDOj4LJ5FPTtKY/eRf+faIyvSKqwnhX/HmuSI+B9MqXVsoMKmPJ37jV1YuAKq3Fww7O836d/vP6t4sw2E71sZTE7PDawUuALjdYSZraLh/LhH8Q==
Incorrect. "$$\widehat{p}$$" is the symbol for population proportion.
Correct. "$$\widehat{p}$$" is the symbol for population proportion.
Incorrect. Try again.
2

### Question 1.4

Incorrect. $$\widehat{p}$$ = $$\frac{39}{300}$$ = 0.13
Correct. $$\widehat{p}$$ = $$\frac{39}{300}$$ = 0.13
Incorrect. Try again.
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4:12

### Question 1.5

RDgz4BtMEqddeIPlscedSC1IMA6C4wLGhXzVVm4xmg5+4eyRuykOD9JFkRy4mooa0wWd59/OZVTyoL3uVwgMMhuu4gWojZqHDCc4UvzHPnj1KBL1p8Nm0KISzuqJe3ql6vPrGBdl7tSBm1Ypk9kNcv+Cp8XZqgJwHfX51y8Wcd8hHZ0nif7FN8+VOFQ9Ypp2l5J1yWjOdM6BZSe0C3/svwg9N3jJoehdfziVAJudlZJbMyyccD51pth2Ui9Nhw65fnOdllV3zP7nhLhFwXsOdmEofujRrN0NTnS8yKxrcWw2BxEFxVGqjs3tRJdGviMc
Incorrect. Since 13% is the percent from a sample, it is a statistic, not a parameter.
Correct. Since 13% is the percent from a sample, it is a statistic, not a parameter.
Incorrect. Try again.
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5:22

### Question 1.6

Incorrect. The sampling distribution of $$\widehat{p}$$ is the distribution of $$\widehat{p}$$'s from all possible samples whereas the sampling distribution of $$\overline{x}$$ is the distribution of $$\overline{x}$$'s from all possible samples. One further difference not given in the answers: The responses of the population from which we sample to get $$\widehat{p}$$'s are categorical whereas the responses of the population from which we sample to get $$\overline{x}$$'s are quantitative. But the sampling distributions do not consist of categorical or quantitative data, but either $$\widehat{p}$$'s or $$\overline{x}$$'s.
Correct. The sampling distribution of $$\widehat{p}$$ is the distribution of $$\widehat{p}$$'s from all possible samples whereas the sampling distribution of $$\overline{x}$$ is the distribution of $$\overline{x}$$'s from all possible samples. One further difference not given in the answers: The responses of the population from which we sample to get $$\widehat{p}$$'s are categorical whereas the responses of the population from which we sample to get $$\overline{x}$$'s are quantitative. But the sampling distributions do not consist of categorical or quantitative data, but either $$\widehat{p}$$'s or $$\overline{x}$$'s.
Incorrect. Try again.
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6:25

### Question 1.7

0PgYlPuuEesLfTDU50NN9HDuAutSxLYIYJPj7DWTVYZWqhYOgZURlV6R6fOgYvWGa03KT9u2MIlFkR3u0wbfe3Of510H6sb7wpsMs948PCm4QOYVPz0p3t5XGM698yatCCYcnAmqdlfr4bulGXnp9qaFT0yYn/f1YmcALLlO1qmDb2tZwuqlEaZLfzxtlZ8K5oA35xQyuG1FIa20Ou/NgrxuAui/4ypqjIc2wZ0QmmOIEbn/dfsXJK2RA9TliMp8DIRT4LqFWWLr0ztL4GdtJw==
Incorrect. Since we have a histogram of $$\widehat{p}$$'s, we note shape, center and spread.
Correct. Since we have a histogram of $$\widehat{p}$$'s, we note shape, center and spread.
Incorrect. Try again.
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7:21

### Question 1.8

Incorrect. For each voter we recorded whether he/she voted for Douglas. This response is categorical. Note: We needed a categorical response variable so that we could demonstrate concepts about proportion.
Correct. For each voter we recorded whether he/she voted for Douglas. This response is categorical. Note: We needed a categorical response variable so that we could demonstrate concepts about proportion.
Incorrect. Try again.
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7:38

### Question 1.9

Incorrect. The parameter for this example is the proportion of all voters who voted for Douglas.
Correct. The parameter for this example is the proportion of all voters who voted for Douglas.
Incorrect. Try again.
2

9:04

### Question 1.10

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Incorrect. The balance point of the histogram is at about 0.21.
Correct. The balance point of the histogram is at about 0.21.
Incorrect. Try again.
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### Question 1.11

4/sxhmgNvrunrgKyuRCmPBXdjUAUW+zGL/2SRCd6ln1RGuENg7y/5OAz/5W3UIjAuMdRl9IcSMESs6eQT3i7kX9tNdvv/LVn7xHZUxVinl6N9WeDyF/bEQ==
Incorrect. While the shape of the histogram initially appears somewhat bell-shaped symmetric, it is still slightly right skewed. And this is important.
Correct. While the shape of the histogram initially appears somewhat bell-shaped symmetric, it is still slightly right skewed. And this is important.
Incorrect. Try again.
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10:43

### Question 1.12

g0xQlpx0SsDUx6k3/swrs9XqibKolXOOGqhU1lMHX7CHTtBm0jHZbcoJZrHrZ2/5fruJhS9kbbk4m30QMg6KCdqNfDRURuVB1ZR5mwuggcVP4GOb9fD6HPFrN61FKzHOo5xjcMW7X790OGuM3EvXQmvW3vu/aMBMvw/i9CCKYaW43lcyKcllygkSu9vI6Qa4NiLy0mgqpWk3NP6+B9IQE9Cq/1GSsGlli217oKkXXkWStESqBRXJA+Zdxh+m+7lQNf3zePJfdT8DO1qnblwm4EHgoKbSxE/jZlHmKA==
Incorrect. The opposite is correct. The estimated sampling distribution of $$\widehat{p}$$ for samples of size 400 is much closer to Normal than the estimated sampling distribution of $$\widehat{p}$$ for samples of size 40.
Correct. The opposite is correct. The estimated sampling distribution of $$\widehat{p}$$ for samples of size 400 is much closer to Normal than the estimated sampling distribution of $$\widehat{p}$$ for samples of size 40.
Incorrect. Try again.
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11:45

### Question 1.13

OFHtoB8rMh3/CFsNE5MsW8F3SKOdxRdz2DEH9EDODMxS43or0SIvI1pxqxWVvSRn+YhD0XXFiRLvg9wt8X10HLZ0YSw7biMrzMSfrkkXX247dYLgnT6XZ5GS1CzpnKvEhtrN1wARTeq5bOoIsGplAje8YhRb0P8VITefozzLWIEKHPxbuekluFmVtyX48IWzLe21U8xEF4qs/tc/2KnCzvUVEM3/zZAlBpv+2ES1MOw=
Incorrect. As sample size increases, the spread of the sampling distribution of $$\widehat{p}$$ decreases.
Correct. As sample size increases, the spread of the sampling distribution of $$\widehat{p}$$ decreases.
Incorrect. Try again.
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### Question 1.14

2MgcqqHR8vmr3itjTnxplM4M4nYGsYxhMPafwxagVGPswbYe1grFvF3wR78Vci8KEqF+DAcNvPJLj7ZDz17H6g2MymZZ8fDtvSWhaQ4MZliszgWkRGnnQ/G4PXZI4PVKEDKTFIp9u1V4+ELoKZyfpriJ//Aqu2tw/DANZnDRYIm8wzNmBJpKy+m6fbtFJ4FS6sJDV5UXFlQagTnviehxUrR4svqY5Bt+5fbatHvAU8p8WsKBH/BG/A==
Incorrect. As sample size increases, the shape of the sampling distribution of $$\widehat{p}$$ gets closer to Normal.
Correct. As sample size increases, the shape of the sampling distribution of $$\widehat{p}$$ gets closer to Normal.
Incorrect. Try again.
2

12:12

### Question 1.15

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Incorrect. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas.
Correct. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas.
Incorrect. Try again.
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14:00

### Question 1.16

FiyghN7iVa2NdAVYTFP1WBUDvfpaIwMwQmzbSB33RLsUIInjuAlkq91tPP1mQ18jxzvULMpFtHUJ9so9Yb4r8w+vC2xOZAp2MT1EiQb3Ex/MXWEmsgqmfzPwaqPFFsXoE9Ho8PMTJmQ96X3ZFSpXphOVGukOAkiFCapfNtMcd4N1De2283/p5YRJAArDhdZw6RsV4RXCBmU0TJzfWHFqBL/lW4fq15PlWmm2JExS/So=
Incorrect. The shape of the estimated sampling distributions of $$\widehat{p}$$ for samples of size n = 40 and n = 400.
Correct. The shape of the estimated sampling distributions of $$\widehat{p}$$ for samples of size n = 40 and n = 400.
Incorrect. Try again.
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14:48

### Question 1.17

S58Oj2bZpt4IuT2lFR/K+pHQxwbARVIXM9mulon/Xh4SdwEuNxH9O18NEL4ri4lILO7qrd8H8w0rHA20aVT0lXKPQ9d0ZBOOYr9CuVDLF4poXaF+gTe0OoNGTrLcpw8gHjBh+g/XOOUKYqTMtt5pqQa3P8fuDbitD0QOtp77we4OdmtUIOx697uSD+Gneeyew2/yvk9sZdRGE8oVKg+Ypg==
Incorrect. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas. This is the key to the differences between the sampling distributions.
Correct. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas. This is the key to the differences between the sampling distributions.
Incorrect. Try again.
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16:11

### Question 1.18

Incorrect. The mean of the sampling distribution of $$\widehat{p}$$ is p = 0.21.
Correct. The mean of the sampling distribution of $$\widehat{p}$$ is p = 0.21.
Incorrect. Try again.
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16:55

### Question 1.19

Incorrect. The standard deviation of the sampling distribution of $$\widehat{p}$$ is $$\sqrt{ \frac{0.21(1-0.21)}{100} }$$.
Correct. The standard deviation of the sampling distribution of $$\widehat{p}$$ is $$\sqrt{ \frac{0.21(1-0.21)}{100} }$$.
Incorrect. Try again.
2

17:38

### Question 1.20

E2yMuXyylSYUCiwmhlAXlqw8FiuwBDxwrkHkYXmkGz8/3zHKXy/dY+Z26LZMTsPX7DSiaP9sqUhF/+zWAaqlbjgZ/eG2PT+aVdSZx6kVqbsIWjibH5nF68+gZWzZeu4eqcwPGpFQK0/Rw61kxIhMrjhCFoHPuH8/VMqcfl1SgMyYb41ObNMcmLf1Y94d63KIhcJKzev7s0uPuhN1oj6xuK/XyTbMm1QPw2hBwjgHBX07SIgVI37LK+2MxJjoYy9ji5KsVhSaG+MMgYi4mf32tTcp5OCEDKYr0uxRZOw+wiuwYWsM9qOnnHfzslyvnd8wflKt3Ude8fcWICCJNYUqllJDidgEzeXvfPEHytvNC8elmBHZ
Incorrect. n = 100 is large enough to apply the Central Limit Theorem and say that the shape is approxiately Normal.
Correct. n = 100 is large enough to apply the Central Limit Theorem and say that the shape is approxiately Normal.
Incorrect. Try again.
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17:55

### Question 1.21

c1YuNSZgIm5tTSB/p7MnO/bKGaugujEPSq69+gR5jMUHuauWcSU0oOd1bsXSwB8D5sYjn7gB0RjEpJwEAvEaOb4peubgW1zKS5CJRRi5R4YMWBxffcN0BsnJkV4dT3S7tM99ivZqFjnN5xjqjTsovKOk6i4ofyw7Qwm+6Lr+JPGQD/+98nJsoqyHCLKmPxyd7JA0e9IKO/m1pl8Jm0ZcKLmASq1Fq/s5
Incorrect. Standard deviation for the sampling distribution of $$\widehat{p}$$ depends on the value of p.
Correct. Standard deviation for the sampling distribution of $$\widehat{p}$$ depends on the value of p.
Incorrect. Try again.
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18:52

### Question 1.22

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Incorrect. This is a correct statement.
Correct. This is a correct statement.
Incorrect. Try again.
2

20:31

### Question 1.23

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Incorrect. "n large" for applying the Central Limit Theorem depends on both np and n(1 - p); both must be 10 or larger.
Correct. "n large" for applying the Central Limit Theorem depends on both np and n(1 - p); both must be 10 or larger.
Incorrect. Try again.
2

22:25

### Question 1.24

Incorrect. p for Lincoln at p = 0.40 is closer to 0.5 than p for Douglas at p = 0.21.
Correct. p for Lincoln at p = 0.40 is closer to 0.5 than p for Douglas at p = 0.21.
Incorrect. Try again.
2

### Question 1.25

Incorrect. np and n(1 - p) must both be bigger than 10 in order to use the Normal approximation.
Correct. np and n(1 - p) must both be bigger than 10 in order to use the Normal approximation.
Incorrect. Try again.
2

22:59

23:03

### Question 1.26

Rz1iaTSExb5n9Ajr+gpCMYW+8oUtR68OlB2ywIVXrk7hnAnsW94N0FhOv4WFsuiRfqZJbaGSejWi2XNU7Mi4MoyIqfCfvxgfZc0NT30CJOsOOvK4WTr8RAhHW3sf3PMnJ1x7ZhltZ9wwrO7aNbxVoINbD/s5PitaWhp5tq7Gn5hKabPC
Incorrect. This is the essence of the Central Limit Theorem for proportion.
Correct. This is the essence of the Central Limit Theorem for proportion.
Incorrect. Try again.
2

25:12

### Question 1.27

Y+vJH7RHv1FFCqtnU7v0spTEyWagd34a+4MSrfld36853Ky5A/9v41zY9cxqFx0kzERK24/Cmjb6dguUBmw4gHAnke9oh4QKUzyFBJXbFzDSYLG8JW22jRE/5L3yT4dg4s7Ag9hnfzo8cledXKWsXrjo8bfGfs/js2lhA1BjJD078GxgUFPhtb3QMd9ZUEfWSBUFlThurkMDShmOTC2Udgs0ObyZrF8f8uPllI7nIqg771s2nA1NWQGBk/1HNdHYUf4VwtPh7pLx/Q6CEAo9ollCU0UJ8vWlAFUlvw==
Incorrect. np and n(1 - p) must both be bigger than 10 for the sampling distribution of $$\widehat{p}$$ to be approximately Normal.
Correct. np and n(1 - p) must both be bigger than 10 for the sampling distribution of $$\widehat{p}$$ to be approximately Normal.
Incorrect. Try again.
2

26:46

### Question 1.28

P/njWrL9RwejMja2dx3okuW8Hht7ClFJ7n+KF4rAcPTX8mEw20PRShezEfOEq5s+Ogp/cYhLl+edrZkj8dJbpVzXmtcSUho6xH/+rxJjeNYZI8GmiWZU5v8Tku8DfPGRAFcZJQ==
Incorrect. The z-score of 6.00 is off the chart and the P-value is essentially zero. This is so small that we can reject H0.
Correct. The z-score of 6.00 is off the chart and the P-value is essentially zero. This is so small that we can reject H0.
Incorrect. Try again.
2

29:16

### Question 1.29

uSdYefRnaX6cv7Uf0sSagD7C9WzkX1KTa6y9rl1ikO/fNVFGOG1EA8oSBOpgaWnJyLMBuWjTC0x0Xd6zvCHK0eP2DB3uOGLeiT8F2wzSnPprOXyWE+R564cnnypxy4uhLp20wecIaQgQieezL9sJwC0xxJS+L8vb4KI4InCyha6ZSTwDfWK7mFJjqWWKiGjxsEwprO0C1bz98rsEVirSmMIKkWVkmXSM6xiYXBwraP3N8hAM5umqj6ZnmTg7g/qogH/07BTY9GwehSWKfJ2Ng+mzIHSQMOQreDeN/Rwz8DbiacW6a6/1BQ==
Incorrect. We compute proportions for categorical data; we have to have quantitative data in order to compute a mean and a standard deviation.
Correct. We compute proportions for categorical data; we have to have quantitative data in order to compute a mean and a standard deviation.
Incorrect. Try again.
2

29:38

### Question 1.30

THv0MT+Ry40a3sKo3a+vtJXGj2bI3uwhbvCx15FyaH9PkcxCHhKsJChcPfSZQbQFdijBYXLGP71tHqLwlSjnd70CvdvjacaepmEbMmR+bEgj8VCUD8eFXarcsdexF+PKJPYCphcJP44Ue9EsR5eoWPlIOZKJVGES
Incorrect. A bar graph is used to display categorical data; a histogram, a boxplot and a stem and leaf plot can be used to display quantitative data.
Correct. A bar graph is used to display categorical data; a histogram, a boxplot and a stem and leaf plot can be used to display quantitative data.
Incorrect. Try again.
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