Question
A 95% confidence interval for u is computed to be (1.55, 4.20). For each of the following hypotheses, state whether Hv0 will be rejected at 0.05 level.
Hv0 : u=2 versus Hv1 : u does not = 2
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Hv0 : u=2 versus Hv1 : u does not = 2
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Answers
Answer
Hv0 : u = 3 versus Hv1 : u does not = 3.
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Answer
Hv0: u=3.4 verus Hv1 : u does not = 3.4
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Answer
Hv0 : u = 2.3 vesus Hv1 : u does not = 2.3
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Since the 95% confidence interval [does/doesnt contain?] uv0, then Hv0 [can or cant?] be rejected at the 0.05 level
Answered by
GPT-4o mini
To determine whether the null hypothesis \( H_{0}: \mu = 2 \) can be rejected at the 0.05 level, we look at the 95% confidence interval for \(\mu\), which is given as (1.55, 4.20).
Since the confidence interval (1.55, 4.20) contains the value 2, we can conclude that:
- The confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 2 \)).
- This means that we **cannot** reject \( H_{0} \) at the 0.05 level because the null hypothesis value is a plausible value within the range of the confidence interval.
Putting it all together, we have:
Since the 95% confidence interval **does contain** \( \mu_0 \), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
Since the confidence interval (1.55, 4.20) contains the value 2, we can conclude that:
- The confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 2 \)).
- This means that we **cannot** reject \( H_{0} \) at the 0.05 level because the null hypothesis value is a plausible value within the range of the confidence interval.
Putting it all together, we have:
Since the 95% confidence interval **does contain** \( \mu_0 \), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
Answered by
GPT-4o mini
To determine whether the null hypothesis \( H_{0}: \mu = 3 \) can be rejected at the 0.05 level, we look at the 95% confidence interval for \(\mu\), which is (1.55, 4.20).
We check if the confidence interval contains the value 3:
- The confidence interval (1.55, 4.20) **does contain** 3.
Because the confidence interval contains the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 3 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
We check if the confidence interval contains the value 3:
- The confidence interval (1.55, 4.20) **does contain** 3.
Because the confidence interval contains the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 3 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
Answered by
GPT-4o mini
To assess the hypothesis \( H_{0}: \mu = 3.4 \) versus \( H_{1}: \mu \neq 3.4 \), we again refer to the 95% confidence interval for \(\mu\), which is (1.55, 4.20).
We check if the confidence interval contains the value 3.4:
- The confidence interval (1.55, 4.20) **does contain** 3.4.
Because the confidence interval includes the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 3.4 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
We check if the confidence interval contains the value 3.4:
- The confidence interval (1.55, 4.20) **does contain** 3.4.
Because the confidence interval includes the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 3.4 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
Answered by
GPT-4o mini
To evaluate the hypothesis \( H_{0}: \mu = 2.3 \) versus \( H_{1}: \mu \neq 2.3 \), we refer to the previously provided 95% confidence interval for \(\mu\), which is (1.55, 4.20).
We check if the confidence interval contains the value 2.3:
- The confidence interval (1.55, 4.20) **does contain** 2.3.
Since the confidence interval includes the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 2.3 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
We check if the confidence interval contains the value 2.3:
- The confidence interval (1.55, 4.20) **does contain** 2.3.
Since the confidence interval includes the value of the null hypothesis, we can conclude:
Since the 95% confidence interval **does contain** \( \mu_0 \) (where \( \mu_0 = 2.3 \)), then \( H_{0} \) **cannot** be rejected at the 0.05 level.
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