MHB Left-Tailed Test Rejects Null Hypothesis at 0.05 Level

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In a left-tailed test, a test statistic of -2 and a shaded area of 0.03 indicate that the null hypothesis can be rejected at the 0.05 significance level. The shaded area represents the p-value, which is the probability of observing a test statistic as extreme as -2 or more extreme under the null hypothesis. In this context, the area of interest is to the left of the test statistic. Understanding the relationship between the shaded area and p-value is crucial for hypothesis testing. This discussion highlights the importance of interpreting shaded areas correctly in left-tailed tests.
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In a left-tailed test, the value of the test statistic is -2. If we know the shaded area is 0.03,
then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.
 
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JocquettaLARuex said:
In a left-tailed test, the value of the test statistic is -2. If we know the shaded area is 0.03,
then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Hi there,

How does the area of the shaded region relate to a p-value in hypothesis testing? In a left-tailed test is the area we look at the area to the left or the area to the right?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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