Questions: Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at least 33 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim contains a statement of equality, it represents the null hypothesis (a) How should you interpret a decision that rejects the null hypothesis? There is sufficient evidence to reject the claim that the mean incubation period for the eggs of a species of bird is at least 33 days. (b) How should you interpret a decision that fails to reject the null hypothesis? There is evidence to the claim that the mean incubation period for the eggs of a species of bird is at least 33 days.

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at least 33 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim contains a statement of equality, it represents the null hypothesis (a) How should you interpret a decision that rejects the null hypothesis? There is sufficient evidence to reject the claim that the mean incubation period for the eggs of a species of bird is at least 33 days. (b) How should you interpret a decision that fails to reject the null hypothesis? There is evidence to the claim that the mean incubation period for the eggs of a species of bird is at least 33 days.
Transcript text: Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null kypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at least 33 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim $\square$ contains a statement of equality, it represents the $\square$ null hypothesis (a) How should you interpret a decision that rejects the null hypothesis? There is $\square$ sufficient evidence to reject $\square$ the claim that the mean incubation period for the eggs of a species of bird is at least 33 days. (b) How should you interpret a decision that fails to reject the null hypothesis? There is $\square$ evidence to $\square$ the claim that the mean incubation period for the eggs of a species of bird is at least 33 days.
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Solution

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Solution Steps

Step 1: Standard Error Calculation

The standard error \( SE \) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{5}{\sqrt{30}} \approx 0.9129 \]

Step 2: Test Statistic Calculation

The test statistic \( Z_{test} \) is computed as follows:

\[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{33 - 33}{0.9129} = 0.0 \]

Step 3: P-value Calculation

For a left-tailed test, the P-value is determined using the standard normal distribution:

\[ P = T(z) = 0.5 \]

Step 4: Hypothesis Test Decision

Given the significance level \( \alpha = 0.05 \):

  • Since \( P = 0.5 \) is greater than \( \alpha \), we fail to reject the null hypothesis.
Step 5: Interpretation of Results

There is not sufficient evidence to reject the claim that the mean incubation period for the eggs of a species of bird is at least 33 days.

Final Answer

The claim represents the null hypothesis. The interpretation of the decision is that there is not sufficient evidence to reject the claim that the mean incubation period for the eggs of a species of bird is at least 33 days.

\(\boxed{\text{Claim represents the null hypothesis; not sufficient evidence to reject the claim.}}\)

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