# What is the rejection rule using the critical value?

If the test statistic is more extreme in the direction of the alternative than the critical value, reject the null hypothesis in favor of the alternative hypothesis. If the test statistic is less extreme than the critical value, do not reject the null hypothesis.

Rejection rule: It is a criterion under which a hypothesis tester decides whether a given hypothesis must be accepted or rejected. The general rule of thumb is that if the value of test statics is greater than the critical value then the null hypothesis is rejected in the favor of the alternate hypothesis.

what is the critical value at the 0.05 level of significance? A sample mean with a z-score greater than or equal to the critical value of 1.645 is significant at the 0.05 level. There is 0.05 to the right of the critical value. DECISION: The sample mean has a z-score greater than or equal to the critical value of 1.645. Thus, it is significant at the 0.05 level.

Consequently, how do you find the critical value?

To find the critical value, follow these steps.

1. Compute alpha (α): α = 1 – (confidence level / 100)
2. Find the critical probability (p*): p* = 1 – α/2.
3. To express the critical value as a z-score, find the z-score having a cumulative probability equal to the critical probability (p*).

How do you determine the decision rule for rejecting the null hypothesis?

For a 5% level of significance, the decision rules look as follows:

1. H0: θ = θ0 versus Ha: θ ≠ θ0 Reject the null hypothesis if test-statistic > 1.96 or if test-statistic < -1.96.
2. H0: θ ≤ θ0 versus Ha: θ > θ0 Reject the null hypothesis if test-statistic > 1.645.
3. H0: θ ≥ θ0 versus Ha: θ < θ0

### What is the critical value in stats?

In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis.

### What is the difference between critical value and test statistic?

The critical value is the value of your test statistic where the p-value coincides with the alpha threshold. A statistic is just a number calculated from data (e.g., a mean, a standard deviation), and a test statistic is a statistic used in a hypothesis test. Let the mean iq of the MIT students be x’.

### What is the critical region in statistics?

1. The critical region. The critical region is the region of values that corresponds to the rejection of the null hypothesis at some chosen probability level. The shaded area under the Student’s t distribution curve is equal to the level of significance.

### What is T critical value?

Critical Value. A critical value is used in significance testing. It is the value that a test statistic must exceed in order for the the null hypothesis to be rejected. For example, the critical value of t (with 12 degrees of freedom using the 0.05 significance level) is 2.18.

### What is the critical value for a 95 confidence interval?

The critical value for a 95% confidence interval is 1.96, where (1-0.95)/2 = 0.025.

### What is the critical value at the 0.01 level of significance?

Hypothesis Test For a Population Proportion Using the Method of Rejection Regions a = 0.01 a = 0.10 Z-Critical Value for a Left Tailed Test -2.33 -1.28 Z-Critical Value for a Right Tailed Test 2.33 1.28 Z-Critical Value for a Two Tailed Test 2.58 1.645

### How do you reject the null hypothesis in t test?

If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis.

### What is a two tailed test?

In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance.

### What does the P value mean?

In statistics, the p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

### What is the decision rule for Chi Square?

Similar to the f test, chi square is treated as a one-tailed, right-tailed test. So the decision rule is to reject ho if the Chi-Square test statistic is greater than 3.84, otherwise do not reject ho. Decision: Since 1.96 is less than 3.84, Do not reject ho. Conclusion: There is insufficient evidence of an unfair coin.