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# Various question about hypothesis testing

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Address Questions 2 on page 1 (see attachment).
Questions 4, 7, 12, and 16 on page 2
Questions 9, 10 on page 3
Questions 12, 16, 18, and 36 a-d on page 4
Questions 40, 42, 44 on page 5
Questions 2 a-c, 4 a-d, and 6 a-d on page 6
Questions 8 a-d, 10 a-f, 12 a-c on page 7
Questions 18, 20, and 22 a-b on page 8
Questions 26 a-b, and 32 a-d on page 9
Questions 34 a-c, 36 a-d, on page 10
Questions 40, and 42 on page 11.

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#### Solution Preview

Please check attachment.

One question needs licensed software to do. Two questions are missing data.

Address Questions 2 on page 1
2. Point estimate=275/785=0.35.
At 95% confidence level, the critical value is 1.96 from standard normal table.
A 95% confidence interval for population proportion is [0.35-1.96*sqrt(0.35*0.65/785), 0.35+1.96*sqrt(0.35*0.65/785)]=[0.317, 0.383]

Questions 4, 7, 12, and 16 on page 2
4. At 95% confidence level with df=17-1=16, the critical value is 2.12 from t table.
A 95% confidence interval for population mean is [3.25-2.12*1.17/sqrt(17), 3.25+2.12*1.17/sqrt(17)]=[2.648, 3.852]
Interpretation: we are 95% confident that population mean is between 2.648 and 3.852.

7. At 95% confidence level with df=40-1=39, the critical value is 2.203 from t table.
A 95% confidence interval for mean length of sentence is [54-2.203*8/sqrt(40), 54+2.203*8/sqrt(40)]=[51.213, 56.787]
Interpretation: we are 95% confident that mean length of sentence is between 51.213 and 56.787.

12. At 99% confidence level with df=40-1=39, the critical value is 2.708 from t table.
A 99% confidence interval for mean amount spent diary is [93.43-2.708*15/sqrt(40), 93.43+2.708*15/sqrt(40)]=[87.007, 99.853]
Interpretation: we are 99% confident that mean length of sentence is between 87.007 and 99.853.

16. A confidence interval can NOT be constructed. Reason: from the box plot (right photo), there is clearly outlier. So the distribution may be not normal.

Questions 9, 10 on page 3
9. The hypothesis is right-tailed because of ">" sign. Parameter being tested is population mean u.

10. The hypothesis is left-tailed because of "<" sign. Parameter being tested is population proportion p.

Questions 12, 16, 18, and 36 a-d on page 4
12. The hypothesis is right-tailed because of ">" sign. Parameter being tested is population proportion p.

16. Let u be the mean charitable contribution per household in the United State in 2005. Ho: u=17072 vs. Ha: u≠17072.
A type I error occurs when ...

#### Solution Summary

The solution gived detailed steps on answering various question about hypothesis testing and confidence intervals using t or normal distribution. All formula and calcuations are shown and explained.

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