b. The test statistic is z = c. The​ P-value is Choose the correct answers below: Because the p-value is less than; greater than; the significance level, fail to reject; reject; the null hypothesis. There is sufficient; insufficient;

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b. The test statistic is z =

c. The​ P-value is

Choose the correct answers below:

Because the p-value is

less than;
greater than;

the significance level,

fail to reject;
reject;

the null hypothesis. There is

sufficient;
insufficient;

 

### Analysis of Polygraph Trial Results

In an experiment involving polygraph tests, 99 trials were conducted, resulting in 24 incorrect outcomes and 75 correct outcomes. We are tasked with testing the hypothesis that the correctness of such polygraph results is less than 80% of the time, at a significance level of 0.05. This involves identifying the null and alternative hypotheses, test statistic, and P-value. We will also provide a conclusion regarding the null hypothesis and derive a final statement about the original claim, utilizing the P-value method and approximating the normal distribution as a substitute for the binomial distribution.

#### Hypothesis Testing

Let \( p \) represent the population proportion of correct polygraph results. Identify the null and alternative hypotheses, and then choose the correct option:

- **A.**  
  \( H_0: p = 0.20 \)  
  \( H_1: p > 0.20 \)

- **B.** (Selected Option)  
  \( H_0: p = 0.80 \)  
  \( H_1: p > 0.80 \)

- **C.**  
  \( H_0: p = 0.20 \)  
  \( H_1: p < 0.20 \)

- **D.**  
  \( H_0: p = 0.80 \)  
  \( H_1: p < 0.80 \)

- **E.**  
  \( H_0: p = 0.20 \)  
  \( H_1: p \neq 0.20 \)

- **F.**  
  \( H_0: p = 0.80 \)  
  \( H_1: p \neq 0.80 \)
Transcribed Image Text:### Analysis of Polygraph Trial Results In an experiment involving polygraph tests, 99 trials were conducted, resulting in 24 incorrect outcomes and 75 correct outcomes. We are tasked with testing the hypothesis that the correctness of such polygraph results is less than 80% of the time, at a significance level of 0.05. This involves identifying the null and alternative hypotheses, test statistic, and P-value. We will also provide a conclusion regarding the null hypothesis and derive a final statement about the original claim, utilizing the P-value method and approximating the normal distribution as a substitute for the binomial distribution. #### Hypothesis Testing Let \( p \) represent the population proportion of correct polygraph results. Identify the null and alternative hypotheses, and then choose the correct option: - **A.** \( H_0: p = 0.20 \) \( H_1: p > 0.20 \) - **B.** (Selected Option) \( H_0: p = 0.80 \) \( H_1: p > 0.80 \) - **C.** \( H_0: p = 0.20 \) \( H_1: p < 0.20 \) - **D.** \( H_0: p = 0.80 \) \( H_1: p < 0.80 \) - **E.** \( H_0: p = 0.20 \) \( H_1: p \neq 0.20 \) - **F.** \( H_0: p = 0.80 \) \( H_1: p \neq 0.80 \)
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