Answer:

Scenario 1:

The scenario provides the following information:

Sample mean (x̄) = 253

Sample size (n) = 50

Population standard deviation (σ) = 16

Level of significance (α) = 0.05

Step 1: State the null and alternative hypotheses

Null Hypothesis (H0): The population mean is equal to 253.

Alternative Hypothesis (Ha): The population mean is not equal to 253.

Step 2: Select a level of significance

The level of significance is given as 0.05.

Step 3: Select the test statistics

Since the population standard deviation is known, we can use the z-test statistics.

Step 4: Formulate the decision rule

The decision rule is formulated based on the level of significance and the critical value of the z-test statistics. For a two-tailed test at α = 0.05, the critical value for z is ±1.96.

Step 5: Compute the value of test statistic

The test statistic for the sample mean is calculated as:

z = (x̄ - μ) / (σ / √n)

z = (253 - 253) / (16 / √50)

z = 0

Step 6: Make a decision

Since the calculated value of z (0) falls within the acceptance region (-1.96 to +1.96), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that the population mean is not equal to 253 at a significance level of 0.05.

Conclusion:

Based on the given information and the computed test statistic, we fail to reject the null hypothesis that the population mean is equal to 253 at a significance level of 0.05.

Step-by-step explanation:

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