Answered

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Determining Whether a Difference Is Statistically
Significant
You calculated the standard deviation of the sample mean differences to be 0.69. You also
calculated the sample mean difference to be 1.74. Now you'll determine whether the
difference is significant. For the purpose of constructing the confidence interval, assume that
there's no difference between the population means.



Options for 1) -3.44, -1.26, -1.38, -3.48

To

Options for 2) 3.44, 1.26, 1.38, 3.48

Word options: within or outside

Determining Whether A Difference Is Statistically Significant You Calculated The Standard Deviation Of The Sample Mean Differences To Be 069 You Also Calculated class=

Sagot :

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:

[tex]\overline{x} \pm zs[/tex]

In which:

  • [tex]\overline{x}[/tex] is the difference between the population means.
  • s is the standard error.

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

The estimate and the standard error are given by:

[tex]\overline{x} = 0, s = 0.69[/tex]

Hence the bounds of the interval are given by:

[tex]\overline{x} - zs = 0 - 1.96(0.69) = -1.38[/tex]

[tex]\overline{x} + zs = 0 + 1.96(0.69) = 1.38[/tex]

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 https://brainly.com/question/25890103

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