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1 answer:
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Answer:
The p-value is 0.0229
Step-by-step explanation:
With we have an upper-tail alternative. Because the p-value is defined as the probability of getting a value at least as extreme as the value observed. The observed value is given by the test statistic z = 1.997 which comes from a standard normal distribution. Therefore, we compute the p-value in the following way P(Z > 1.997) = 0.0229, i.e., the p-value is 0.0229
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.
1 - To solve, we just use algebraic operations:
2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
Are:
3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:
So, the solutions are:
