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alexandr402 [8]
2 years ago
7

Determining Whether a Difference Is Statistically

Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
6 0

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.

<h3>What is the z-distribution confidence interval?</h3>

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

#SPJ2

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