Question

Determining Whether a Difference Is Statistically

Answer 1

Using the z-distribution, it is found that:

• The 95% confidence interval is of -1.38 to 1.38.

• The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.

What is the z-distribution confidence interval?

The confidence interval is:

$\overline{x} \pm zs$

In which:

• $\overline{x}$ is the difference between the population means.

• s is the standard error.

In this problem, we have a 95% confidence level, hence$\alpha = 0.95$, z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$, so the critical value is z = 1.96.

The estimate and the standard error are given by:

$\overline{x} = 0, s = 0.69$

Hence the bounds of the interval are given by:

$\overline{x} - zs = 0 - 1.96(0.69) = -1.38$

$\overline{x} + zs = 0 + 1.96(0.69) = 1.38$

1.74 is outside the interval, hence:

• The 95% confidence interval is of -1.38 to 1.38.

• The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.

More can be learned about the z-distribution at brainly.com/question/25890103

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