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You wish to test the following claim H^Ц at a significance level of а=0.10. For the context of this problem. Ц₄=Ц₂-Ц₁ where the first data set represents a pre-test and the second data set represents a post-test.
Hₐ² Ц =0
Ha² Ц ≠0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-4est simples for n=25 subjects. The average difference (post - pre) is d=-34.3 with a standard deviation of the differences of sd=42.9.
What is the critical value for this test? (Report answer accurate to three decimal places.) critical value . ± ____

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
fest statistic = ____

You Wish To Test The Following Claim HЦ At A Significance Level Of А010 For The Context Of This Problem ЦЦЦ Where The First Data Set Represents A Pretest And Th class=

Sagot :

  • The critical value for this test is of: t = ±1.7109.
  • The test statistic for this test is of: t = -4.  

How to obtain the critical value for the test?

We have a two-tailed test, as we are testing if the mean is different of a value.

The t-distribution is used, as we have the standard deviation for the sample, and the parameters are given as follows:

  • 25 - 1 = 24 degrees of freedom.
  • Significance level of 0.10.

Using a t-distribution calculator, the critical value is of:

t = ± 1.7109.

How to obtain the test statistic?

The equation for the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In the context of this problem, the values of these parameters are of:

[tex]\overline{x} = -34.3, \mu = 0, s = 42.9, n = 25[/tex]

Hence the value of the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-34.3 - 0}{\frac{42.9}{\sqrt{25}}}[/tex]

t = -4.

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

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