# Chapter 1. The Reasoning of Statistical Estimation

true
Stat Tutor
true
true

1:14

### Question 1.1

Z+q5ye8TsXODMwLG+KC25oE2H9hNrRApp+jPxO3b7RX8NuCwMiCArrDb4I3e9CglkrCMlKnpBH2PJXipMJ1u5qXBbaipqs6IQgig3ulFOBbiHj0Mjy13+hG8WXJeI2QVOOU9qW0IJugqByCoHwXqc/YBhkXrC6gdNNbuIPtYQNSF7tJSt4yhayQFCJb2K6VVqHBPA/bmsl08EYzkzbzMreW6zwE0NGXb6qwVCuOZR2cVqNn/uSCy79eQ6L3RCklwRjJyaGv5/xZOBRytOsPPo+t5aHk=
Incorrect. Since $$\overline{x}$$ does not equal µ, we have to know how accurately it estimates µ. In other words, we need a measure of the error, i.e., a measure of how far off $$\overline{x}$$ could be from µ.
Correct. Since $$\overline{x}$$ does not equal µ, we have to know how accurately it estimates µ. In other words, we need a measure of the error, i.e., a measure of how far off $$\overline{x}$$ could be from µ.
Incorrect. Try again.
2

3:58

### Question 1.2

yAXtNY9HeXR6mYtKI2Qt4b8kHGCmtRibZZQvuF+4cEj++vLucd6+IegYR8WztX0gauOPEFjpwAUygl/7MBy1VJ8UiUkpb4dDKrHRfPXGTVOByRRfXPhQZmwPM599VjSlJq3bwuChP4BfcuG0Pm5ApaJtveabkHd/oF8vKVNJggFiXwyZ
Incorrect. Before taking a sample, we do not know the value of $$\overline{x}$$ so we can talk about the probability of $$\overline{x}$$ being in some interval. But after we take a sample, we know the value of $$\overline{x}$$ and we have "confidence" that this value is in an interval.
Correct. Before taking a sample, we do not know the value of $$\overline{x}$$ so we can talk about the probability of $$\overline{x}$$ being in some interval. But after we take a sample, we know the value of $$\overline{x}$$ and we have "confidence" that this value is in an interval.
Incorrect. Try again.
2

5:50

### Question 1.3

9UD5+h75sCD9+Yv4lseG5U0MgIPmKa5nR451SZ35udUrSqNv11zqNvJdJehP+tOc3FbK/OnwxNBZGFfA8trqF8+Oj9u4COGSFRGCP+hbmcWtyXAwlEcAXN3MI/ScgFv1L9fCDTThZF9MQQLxE1IdokarAasfTMEUAuhAh3Lrb0Lf8AO48CeHibO7CNASyZmwDL7LIiWmCD3+ghTuTu9/LpgNyebWS4RuYMhESg==
Incorrect. The sampling distribution of $$\overline{x}$$ provides us with probabilities on $$\overline{x}$$ and a measure of the variability of $$\overline{x}$$ with the standard deviation of the sampling distribution of $$\overline{x}$$. We use both of these to find margin of error.
Correct. The sampling distribution of $$\overline{x}$$ provides us with probabilities on $$\overline{x}$$ and a measure of the variability of $$\overline{x}$$ with the standard deviation of the sampling distribution of $$\overline{x}$$. We use both of these to find margin of error.
Incorrect. Try again.
2

6:17

### Question 1.4

r12KGkFk6z0bPeydQrNimLz4arVSkj0sLS+EJcryXd7A1ZGwH/MliCtrMel3AAmS399f2SsdWOkienaIy0IzyznNMYa8yY5bgDTy4L8Z2nqOVcifZE3ZEVv4AkNbHcp8j890malb//X1xIeWmuBJXsZhklkE7rAuEwgDIlWR9P2hCrxaTGICRtl6dMsKz3mA
Incorrect. This is a correct statement.
Correct. This is a correct statement.
Incorrect. Try again.
2

### Question 1.5

rL0/u3ajpgkrt69puWy4x5hH5lWZOkR1LTvmORdt9jts9NNcVB7eifJrbzPoez7h/u+JH7RWHgNucL7xca9XmXJhv+jYkkW3XNbXOQhYQlFNXABz2NuH+QGTI/UcYx9ujqxlgbVaryaKEQA6R/wvpbGcTgkKA3a1PZ/hMl1qwe8gjwLV+pMpZT5IigWu4xJPWaWFQtUcMBo4+omzBbJqP9bT2dBbcU9FpOSr+QmNSrq4bYfqGY1FFcmUMIul/QdcDB7iYYmKzeTeTgiEHnYvKaSaCVnceV/FAhsIXkUJkMMA2O8bFfZGfvstSS7FB8fN6I+DZzQZss8bXTKMaM7xXLAXJPvuECdo
Incorrect. We use $$\overline{x}$$ to estimate µ. But since the value of $$\overline{x}$$ does not equal the value of µ, we have error. Margin of error is a measure of this error.
Correct. We use $$\overline{x}$$ to estimate µ. But since the value of $$\overline{x}$$ does not equal the value of µ, we have error. Margin of error is a measure of this error.
Incorrect. Try again.
2

9:31

### Question 1.6

YMVnBBij8p+Nikojv2b2Ld85yQK/Bkg2Yr7uot4Dx0CATJ1a6XRHYy0Msbe8epTpfzMWblbRBpzOTajgCYs4gj71wA4D9Y7XFavfrJ1iyJ1ppvJ/X5z4hL0atcBnBzpGugOSpGnp6hghJfQq1bDOtkfs+M4lNibeFEvPIVuJjT8RMSWDMzkYlJcDWaJ5qcuR88Ho3s2Hvi8+ENLXHkXcKGPCnZUIA+oXY2OB9fwK4k79S9VFmUyn96rwZTccu5Lg
Incorrect. A confidence interval is an estimate of the value of a parameter. It is not intended to tell us a range of values for the data.
Correct. A confidence interval is an estimate of the value of a parameter. It is not intended to tell us a range of values for the data.
Incorrect. Try again.
2

### Question 1.7

Incorrect. This is exactly how we compute a confidence interval estimate for µ.
Correct. This is exactly how we compute a confidence interval estimate for µ.
Incorrect. Try again.
2

### Question 1.8

0yA0Gz36U3TYRhPxhm/vqtdWp8MHWWw3q9V/rtUUBPXSOQAZd/5v7Uj3VaUYFWm28/gLpBjOgiXI253QLg7Lc1FloYHYdrz8e6rQSiIclPL4hniInaHoDq224AI4ogE7GJiqC5Ayu2ZWdDn0hKWx1X00jncyQlzoQdyzZVFJdMqX5iayVFDodIbq3QZarOLE44Jt8q9ZM0AmbasbDHBrKvXVR4n7ZTrNrqNy+gqV9jFZfkRXKSpx+a4bmMnBggCH
Incorrect. The value of $$\overline{x}$$ is always between $$\overline{x}$$ - ME and $$\overline{x}$$ + ME. We can be 100% confident of that.
Correct. The value of is always between $$\overline{x}$$ - ME and $$\overline{x}$$ + ME. We can be 100% confident of that.
Incorrect. Try again.
2

11:13

### Question 1.9

O4xlfa1oc+UiCw+4dnT7E0qR1Y9giiYxtOmoWGfyTD7IIvSR+T1sKdceRgVq+BPtT1T0+YuInIGVRlQ1Lztx1N7dqDawyeaGWhNtByyn9w7RGK2SXxLPbBYpxq6SODvQlmrJW8uwqwH6a9ghl2Szu2oHGVqN0gv06idHkK4ztmYYdMtilafiktO4wfeU3yTUQoggLc2pSmcFORMEr1svyHOP7AuvipqcZ5FEV9jO9HAIycIOFVjseYQjRJSj1qk+UfAQaOTBYJ11q58y9koHfBI6BTnYao8+LzMKlnMqvoJmEiQSqtNQbAAES8vqhRk+hizEZpqJmbp6W8HkBDxX4cm9xqMGqy/hZD0YygtgyqLjAeVRuk9u3uQ1auJMNOTGFZx6ECAZlH4xZiFalgXZ2umsQ0Rl9fmQmm5wKZK2gAt+MVtzyJkIOLudIqA=
Incorrect. If $$\overline{x}$$ is between µ - ME and µ + ME, then µ will be between $$\overline{x}$$ - ME and $$\overline{x}$$ + ME.
Correct. If $$\overline{x}$$ is between µ - ME and µ + ME, then µ will be between $$\overline{x}$$ - ME and $$\overline{x}$$ + ME.
Incorrect. Try again.

### Question 1.10

4UHl9JCWRXpof4mkpijEWLEH4kvSi1gfkCFXb6f7zgkW2U4KHm7xW9SNSq9Uj0u204gC97wicOSMXONXYA+TiVxoic5m9MM0fD1cTJoswaHS+F/6YGq46KviGBOvrq2q15BkWcbT+HKO2opVsIPelDcWRB2e8skpPka/vdV78yFPIRTMZ2TpeLsb9QnWfJH3eWpirtmxhzYmzRVot0/kxfUURKSORdtE/lIn1Kgjy1+co9dldkvwRRxAolhhyrAvz4k1jrEOoga/DqrPK5T98hevFE05+su9FfXtbv/fDlQjU1BxKXcKFtSS3nl3kD1F
Incorrect. This is the idea behind a confidence interval. Just like the stake is invisible, the value of the parameter µ is unknown. We can compute margin of error similar to knowing the length of the rope. And we know the value of $$\overline{x}$$ just like we know where the goat is. Using this information, we can get a good idea of where the stake is, i.e., we can get an estimate of what the value of µ is.
Correct. This is the idea behind a confidence interval. Just like the stake is invisible, the value of the parameter µ is unknown. We can compute margin of error similar to knowing the length of the rope. And we know the value of $$\overline{x}$$ just like we know where the goat is. Using this information, we can get a good idea of where the stake is, i.e., we can get an estimate of what the value of µ is.
Incorrect. Try again.
2

11:59

### Question 1.11

ud+6p75YIRatvXQz6G8wocJeLLVfwY5p+QqPuYsXMi7cjWBRILIse+E4EIbd29IzrgeUH5zViruucKkMZ6g8eXcq1OPFSNgluIly4tKupLsafMRwPTv4qTWsy4gGAttj4UrqQG3Bz6BQ+SgkzYUyqHQZ4fvuWTZQ9BySTLTKzsR6VL/My9w12ZaO6kCCogiwYJXEhnA0/B//EtkPSdG0KOeJ3EU3mC/yr19XON4llTg0r14NkL3rYiSM11lEW/hpiHCyej/oHyk=
Incorrect. This applet is intended to demonstrate this important fact.
Correct. This applet is intended to demonstrate this important fact.
Incorrect. Try again.
2

12:28

### Question 1.12

Incorrect. The interval ($$\overline{x}$$ - ME, $$\overline{x}$$ + ME) is a confidence interval estimate for µ, so it gives us a range of feasible values for µ.
Correct. The interval ($$\overline{x}$$ - ME, $$\overline{x}$$ + ME) is a confidence interval estimate for µ, so it gives us a range of feasible values for µ.