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Is the ideal number of children equal to 2, or higher or lower than that? For testing that the mean response from a recent survey equals 2.0 for the question, “What do you think is the ideal number of children to have?” The following output is obtained from a standard statistical software package:

Report the test statistic value and show how its value was obtained from the other values reported in the table (5 marks)
In 1-2 sentences at most, explain what the p-value represents and interpret its value (5 marks)

User Miaonster
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Answer:

Hi<3

Step-by-step explanation:

To assess whether the ideal number of children is equal to 2, you would typically perform a hypothesis test on the mean response from a survey. Assuming you have the output from a statistical software package, you would focus on the test statistic and the p-value.

1. **Test Statistic:**

The test statistic is a measure of how many standard deviations a data point or sample mean is from the population mean. In this context, you should look for a t-statistic or z-statistic depending on the type of test conducted (t-test or z-test).

2. **Calculation of Test Statistic:**

- For a t-test, the formula is often \( t = \frac{{\bar{x} - \mu}}{{s/\sqrt{n}}} \), where \(\bar{x}\) is the sample mean, \(\mu\) is the hypothesized population mean (in this case, 2.0), \(s\) is the sample standard deviation, and \(n\) is the sample size.

- For a z-test, the formula is similar but uses the population standard deviation instead of the sample standard deviation.

3. **P-value Explanation:**

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true. In this case, the null hypothesis might be that the true mean ideal number of children is 2.0. A low p-value (typically below a significance level like 0.05) suggests that you can reject the null hypothesis.

4. **Interpretation of P-value:**

- If p-value ≤ 0.05: You would reject the null hypothesis and conclude that there is evidence to suggest that the ideal number of children is different from 2.

- If p-value > 0.05: You would fail to reject the null hypothesis, indicating that there is not enough evidence to conclude that the ideal number of children is different from 2.

Remember, the choice of significance level (e.g., 0.05) is arbitrary and depends on the researcher's judgment or convention in the field.

User Menelaos Vergis
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