use a,b,c,d,e to answer number 8 **Statistical Exercises: Hypothesis Testing with Normal Approximation**In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part I of this section). Assume a 0.05 significance level and answer the following:a. Is the test two-tailed, left-tailed, or right-tailed?b. What is the test statistic?c. What is the P-value?d. What is the null hypothesis, and what do you conclude about it?e. What is the final conclusion? **Public Speaking**A TNS poll of 1,000 randomly selected adults showed that 460 of them say that public speaking is an activity that they dread most. Shown next is the StatCrunch display resulting from a test of the claim that fewer than half of adults say that public speaking is the activity that they dread most.**STATCRUNCH**_Hypothesis test results:_- **p:** proportion of successes for population- **H₀ (Null Hypothesis):** p = 0.5- **Hₐ (Alternative Hypothesis):** p < 0.5| Proportion | Count | Total | Sample Prop. | Std. Err. | Z-Stat | P-value ||------------|-------|-------|--------------|-------------|----------|----------|| p | 460 | 1000 | 0.46 | 0.015811387 | -2.529822| 0.0057 |In this hypothesis test, the null hypothesis (H₀) claims that 50% of adults dread public speaking the most, while the alternative hypothesis (Hₐ) suggests that fewer than 50% dread it. The test results show a sample proportion of 0.46 with a standard error of approximately 0.0158. The Z-statistic is -2.529822, and the resulting P-value is 0.0057, indicating significant evidence against the null hypothesis, supporting the claim that fewer than half of adults find public speaking to be the most dreaded activity.

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Description: use a,b,c,d,e to answer number 8 **Statistical Exercises: Hypothesis Testing with Normal Approximation**In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial di

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In Exercises 5-8, identify the indicated values or interpret the given display. Use the nor- mal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a. Is the test two-tailed, left-tailed, or right-tailed? b. What is the test statistic? c. What is the P-value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion?

In Exercises 5-8, identify the indicated values or interpret the given display. Use the nor- mal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a. Is the test two-tailed, left-tailed, or right-tailed? b. What is the test statistic? c. What is the P-value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion?

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use a,b,c,d,e to answer number 8

**Statistical Exercises: Hypothesis Testing with Normal Approximation**

In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part I of this section). Assume a 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

**Public Speaking**

A TNS poll of 1,000 randomly selected adults showed that 460 of them say that public speaking is an activity that they dread most. Shown next is the StatCrunch display resulting from a test of the claim that fewer than half of adults say that public speaking is the activity that they dread most.

**STATCRUNCH**

_Hypothesis test results:_

- **p:** proportion of successes for population
- **H₀ (Null Hypothesis):** p = 0.5
- **Hₐ (Alternative Hypothesis):** p < 0.5

| Proportion | Count | Total | Sample Prop. | Std. Err. | Z-Stat | P-value |
|------------|-------|-------|--------------|-------------|----------|----------|
| p | 460 | 1000 | 0.46 | 0.015811387 | -2.529822| 0.0057 |

In this hypothesis test, the null hypothesis (H₀) claims that 50% of adults dread public speaking the most, while the alternative hypothesis (Hₐ) suggests that fewer than 50% dread it. The test results show a sample proportion of 0.46 with a standard error of approximately 0.0158. The Z-statistic is -2.529822, and the resulting P-value is 0.0057, indicating significant evidence against the null hypothesis, supporting the claim that fewer than half of adults find public speaking to be the most dreaded activity.

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