Question
A 95% confidence interval for u is computed to be (1.50, 3.05). For each of the following hypotheses, state whether will be rejected at 0.05 level.
Hv0 : u = 4 versus Hv1 : u does not = 4
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Hv0 : u = 4 versus Hv1 : u does not = 4
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Answers
Answer
Hv0 : u = 2versus Hv1 : u does not = 2
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Answer
Hv0 : u = 2.8 versus Hv1 : u does not = 2.8
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Answer
Hv0 : u = 2.3 versus Hv1 : u does not = 2.3
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Does the 95% confidence level contain uvo? Is Hv0 rejected?
Answered by
GPT-4o mini
To determine whether the null hypothesis \(H_{0}: \mu = 4\) will be rejected at the 0.05 significance level, we examine the confidence interval (CI) provided, which is (1.50, 3.05).
1. **Does the 95% confidence interval contain \(\mu_0\)?**
The value under consideration is \(\mu_0 = 4\). Since \(\mu_0 = 4\) is outside the confidence interval (1.50, 3.05), this means that the interval does not contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
Since the value of 4 is not included in the 95% confidence interval, we reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval does **not** contain \(\mu_0 = 4\).
- The null hypothesis \(H_{0}: \mu = 4\) will be rejected at the 0.05 level.
1. **Does the 95% confidence interval contain \(\mu_0\)?**
The value under consideration is \(\mu_0 = 4\). Since \(\mu_0 = 4\) is outside the confidence interval (1.50, 3.05), this means that the interval does not contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
Since the value of 4 is not included in the 95% confidence interval, we reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval does **not** contain \(\mu_0 = 4\).
- The null hypothesis \(H_{0}: \mu = 4\) will be rejected at the 0.05 level.
Answered by
GPT-4o mini
We are examining the hypothesis:
- \(H_{0}: \mu = 2\) (null hypothesis)
- \(H_{1}: \mu \neq 2\) (alternative hypothesis)
Given that the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2\). Since \(2\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2\).
- The null hypothesis \(H_{0}: \mu = 2\) will **not** be rejected at the 0.05 level.
- \(H_{0}: \mu = 2\) (null hypothesis)
- \(H_{1}: \mu \neq 2\) (alternative hypothesis)
Given that the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2\). Since \(2\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2\).
- The null hypothesis \(H_{0}: \mu = 2\) will **not** be rejected at the 0.05 level.
Answered by
GPT-4o mini
We are examining the hypotheses:
- \(H_{0}: \mu = 2.8\) (null hypothesis)
- \(H_{1}: \mu \neq 2.8\) (alternative hypothesis)
Given the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2.8\). Since \(2.8\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2.8\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2.8\).
- The null hypothesis \(H_{0}: \mu = 2.8\) will **not** be rejected at the 0.05 level.
- \(H_{0}: \mu = 2.8\) (null hypothesis)
- \(H_{1}: \mu \neq 2.8\) (alternative hypothesis)
Given the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2.8\). Since \(2.8\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2.8\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2.8\).
- The null hypothesis \(H_{0}: \mu = 2.8\) will **not** be rejected at the 0.05 level.
Answered by
GPT-4o mini
We are examining the hypotheses:
- \(H_{0}: \mu = 2.3\) (null hypothesis)
- \(H_{1}: \mu \neq 2.3\) (alternative hypothesis)
Given the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2.3\). Since \(2.3\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2.3\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2.3\).
- The null hypothesis \(H_{0}: \mu = 2.3\) will **not** be rejected at the 0.05 level.
- \(H_{0}: \mu = 2.3\) (null hypothesis)
- \(H_{1}: \mu \neq 2.3\) (alternative hypothesis)
Given the 95% confidence interval for \(\mu\) is (1.50, 3.05):
1. **Does the 95% confidence interval contain \(\mu_0\)?**
- The value under consideration is \(\mu_0 = 2.3\). Since \(2.3\) is within the confidence interval (1.50, 3.05), this means that the interval **does** contain the value of the null hypothesis.
2. **Is \(H_{0}\) rejected?**
- Since the value of \(2.3\) is included in the 95% confidence interval, we do not reject the null hypothesis \(H_{0}\) at the 0.05 significance level.
In summary:
- The 95% confidence interval **does** contain \(\mu_0 = 2.3\).
- The null hypothesis \(H_{0}: \mu = 2.3\) will **not** be rejected at the 0.05 level.
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