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### **Question 6: Complete the following statements by using the given words below.**

**Word bank:**
- standard normal
- mean
- test statistic
- sample
- reject
- standard error
- null hypothesis
- Type I error
- Type II error
- accepting null hypothesis

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**Statements:**

**(a)** If you accept the null hypothesis when it is true, you make a(n) ____________.

**(b)** In a ____________ probability distribution, the mean is 0 and the standard deviation is 1.

**(c)** The center of a normal curve is the ____________ of the distribution.

**(d)** When *t* is used to estimate *µ*, the margin of error is computed by using the ____________.

**(e)** Larger values of the standard deviation result in a normal curve that is ____________.

**(f)** The objective of statistics is to determine the amount of ____________ of a population parameter on the basis of a sample statistic.

**(g)** For a hypothesis test, we can compare the value of the ____________ to the critical value.

**(h)** The standard deviation of a point estimator is called the ____________.

**(i)** The rejection region of a hypothesis test is the set of values of a test statistic that leads to ____________.

**(j)** The level of significance, in hypothesis testing, is the probability of a ____________.

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### **Solutions:**

**(a)** accepting null hypothesis  
- When you accept the null hypothesis when it is true, you're accepting it correctly.

**(b)** standard normal  
- In a standard normal distribution, the mean is 0 and the standard deviation is 1.

**(c)** mean  
- The center of a normal distribution curve is always the mean.

**(d)** standard error  
- The margin of error when using a *t* distribution is computed using the standard error.

**(e)** flatter and more spread out  
- Larger values of the standard deviation result in a normal curve that is flatter and more spread out.

**(f)** standard error  
- The goal of statistics is to determine the amount of error in a sample statistic used to estimate a population parameter, called the standard error.

**(g)** test statistic  
- The test statistic is compared to the critical value to make a decision in a hypothesis test.

**(h)** standard error  
- The standard deviation of a point estimator is called the standard error.

**(i)** reject  
- The rejection region consists of test statistic values that lead to rejecting the null hypothesis.

**(j)** Type I error  
- The level of significance (α) in hypothesis testing represents the probability of making a Type I error (rejecting a true null hypothesis).

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Would you like further explanations or more details on any of the questions?

### Related Questions:
1. How do you calculate the standard error in hypothesis testing?
2. What is the relationship between Type I and Type II errors in hypothesis testing?
3. Can you explain how to find the critical value in a hypothesis test?
4. What are the key differences between a standard normal distribution and other normal distributions?
5. How does increasing the sample size affect the standard error?

### Tip:
When conducting hypothesis testing, always ensure that the assumptions for your chosen test (like normality for a z-test or t-test) are adequately met to ensure valid results.

Complete the following statements by using the given words below: standard normal, mean, test statistic, sample, reject, standard error, null hypothesis, Type I error, Type II error, accepting null hypothesis.

Explore key concepts in hypothesis testing by completing statements using terms like standard normal, mean, and standard error. This exercise covers hypothesis testing, probability distributions, and error types, essential for introductory statistics courses.

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