The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.      Number of Crimes by Area   A B C D E F G H Before 14 7 4 5 17 12 8 9 After 2 7 3 6 8 13 3 5           Has there been a decrease in the number of crimes since the inauguration of the program? Use the 0.01 significance level. Estimate the p-value.   Compute the value of the test statistic. (Round your answer to 2 decimal places.)

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The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results. 

 

  Number of Crimes by Area
  A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5
 

 

 

 

 

Has there been a decrease in the number of crimes since the inauguration of the program? Use the 0.01 significance level. Estimate the p-value.

 

  1. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

 

 

 

 

 

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Follow-up Question

Can you double check the alternative hypothesis here? Should the sign be flipped to less than? If not, please explain.

 

**Solution:**

The null and alternative hypothesis is

\[ H_0: \mu_d \geq 0 \]

\[ H_1: \mu_d > 0 \]

**Explanation:**

- \( H_0 \) represents the null hypothesis, which states that the mean difference (\( \mu_d \)) is greater than or equal to zero.
- \( H_1 \) represents the alternative hypothesis, which states that the mean difference (\( \mu_d \)) is greater than zero.
Transcribed Image Text:**Solution:** The null and alternative hypothesis is \[ H_0: \mu_d \geq 0 \] \[ H_1: \mu_d > 0 \] **Explanation:** - \( H_0 \) represents the null hypothesis, which states that the mean difference (\( \mu_d \)) is greater than or equal to zero. - \( H_1 \) represents the alternative hypothesis, which states that the mean difference (\( \mu_d \)) is greater than zero.
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