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Answer:
(a) C: 0.0465 ; reject the null hypothesis
(b) B: 0.3409 ; fail to reject the null hypothesis
Step-by-step explanation:
Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;
- If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
- If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.
(a) Now, we are given alternate hypothesis, : p < 3/5
Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;
P-value = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = <u>0.0465</u>
Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>
(b) Now, we are given alternate hypothesis, : p > 0.383
Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;
P-value = P(Z > 0.41) = 1 - P(Z 0.41)
= 1 - 0.6591 = <u>0.3409</u>
Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>
<h3>Answer: Choice A</h3>
- Domain: x > 4
- Range: y > 0
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Explanation:
We want to avoid having a negative number under the square root. Solving leads to
So it appears the domain could involve x = 4 itself; however, if we tried that x value, then we'd get a division by zero error.
So in reality, the domain is x > 4.
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The range of y = sqrt(x) is the set of positive real numbers. So y > 0 is the range for this equation. Shifting left and right does not affect the range, so the range of y = sqrt(x-4) is also y > 0.
We are dividing a positive number (3) over some positive number in the denominator. Overall, the expression is positive because positive/positive = positive.
Therefore, the range of the given equation is y > 0
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The graph is shown below. We have a vertical asymptote at x = 4 and a horizontal asymptote at y = 0. The green curve is fenced in the upper right corner (northeast corner).