Suppose the following plot represents the sampling distribution of a test statistic under two competing hypotheses. The red curve shows the distribution when the null hypothesis, H 0 H_0 , is true, while the blue curve shows the distribution when the alternative hypothesis, H 1 H_1 , is true. The dashed line represents the critical value for a one-tailed hypothesis test. If the test statistic falls to the right of this critical value, H 0 H_0 is rejected.

The shaded regions represent the two types of errors that may occur when making a hypothesis-testing decision.
Which conditional probability represents the red shaded region?

Question

Suppose the following plot represents the sampling distribution of a test statistic under two competing hypotheses. The red curve shows the distribution when the null hypothesis,  H 0 H_0 , is true, while the blue curve shows the distribution when the alternative hypothesis,  H 1 H_1 , is true. The dashed line represents the critical value for a one-tailed hypothesis test. If the test statistic falls to the right of this critical value,  H 0 H_0  is rejected.  
 
 The shaded regions represent the two types of errors that may occur when making a hypothesis-testing decision. 
 Which conditional probability represents the red shaded region?

Answer

P(reject H 0 ​ ∣ H 0 ​ is true)

Answer

P(H 0 ​ is true ∣ reject H 0 ​)

Answer

P(reject H 0 ​ ∣ H 1 ​ is true)

Answer

P(fail to reject H 0 ​ ∣ H 0 ​ is true)

Answer

P(fail to reject H 0 ​ ∣ H 1 ​ is true)

Crowdly

Suppose the following plot represents the sampling distribution of a test stati...

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