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.

Question

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

GPT-4o mini · Answer

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.

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

GPT-4o mini · Answer

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.

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

GPT-4o mini · Answer

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.

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

GPT-4o mini · Answer

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.