For the following significance level, what is the probability of making a Type I error? 0.02 i

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**Question:**

For the following significance level, what is the probability of making a Type I error?

\(\alpha = 0.02\)

**Explanation:**

In hypothesis testing, a Type I error occurs when the null hypothesis is rejected when it is true. The probability of making a Type I error is denoted by the significance level, \(\alpha\). Therefore, at a significance level of \(\alpha = 0.02\), the probability of making a Type I error is 2%.

**Diagram Explanation:**

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Transcribed Image Text:**Question:** For the following significance level, what is the probability of making a Type I error? \(\alpha = 0.02\) **Explanation:** In hypothesis testing, a Type I error occurs when the null hypothesis is rejected when it is true. The probability of making a Type I error is denoted by the significance level, \(\alpha\). Therefore, at a significance level of \(\alpha = 0.02\), the probability of making a Type I error is 2%. **Diagram Explanation:** There is no accompanying graph or diagram in this image.
A random sample of 22 observations taken from a population that is normally distributed produced a sample mean of 58.5 and a standard deviation of 7.5.

Find the range for the *p*-value and the critical and observed values of *t* for the following test of hypothesis, using α = 0.01.

\( H_0: \mu = 55 \) versus \( H_1: \mu \neq 55 \).

Round your answers for the values of *t* to three decimal places.

- \( t_{\text{critical left}} = \) 
- \( t_{\text{critical right}} = \) 
- \( t_{\text{observed}} = \) 

(Note: Ensure to use a t-distribution table or calculator to find the critical values and compute the observed t-value based on the given sample statistics.)
Transcribed Image Text:A random sample of 22 observations taken from a population that is normally distributed produced a sample mean of 58.5 and a standard deviation of 7.5. Find the range for the *p*-value and the critical and observed values of *t* for the following test of hypothesis, using α = 0.01. \( H_0: \mu = 55 \) versus \( H_1: \mu \neq 55 \). Round your answers for the values of *t* to three decimal places. - \( t_{\text{critical left}} = \) - \( t_{\text{critical right}} = \) - \( t_{\text{observed}} = \) (Note: Ensure to use a t-distribution table or calculator to find the critical values and compute the observed t-value based on the given sample statistics.)
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