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 most 44 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 evidence to the claim that the mean incubation period for the eggs of a species of bird is at most 44 days.

Solution Steps

The scientist claims that the mean incubation period for the eggs of a species of bird is at most 44 days. This can be formulated as:

• Null Hypothesis (\(H_0\)): \(\mu \leq 44\)
• Alternative Hypothesis (\(H_a\)): \(\mu > 44\)

From the sample data, we have:

• Sample Mean (\(\bar{x}\)): 45
• Sample Standard Deviation (\(\sigma\)): 2
• Sample Size (\(n\)): 30

The Standard Error (\(SE\)) is calculated as follows: \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{30}} \approx 0.3651 \]

The test statistic (\(Z_{test}\)) is calculated using the formula: \[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{45 - 44}{0.3651} \approx 2.7386 \]

For a right-tailed test, the P-value is calculated as: \[ P = 1 - T(z) \approx 0.0031 \]

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

• Since \(P < \alpha\) (i.e., \(0.0031 < 0.05\)), we reject the null hypothesis.

Final Answer