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Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043.

Keith reads that the mean nap is 22 minutes.

t equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction

The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.

Sagot :

Using the t-distribution, the t-statistic for the two-sided test would be of t = 0.7.

What is the test statistic for a t-distribution hypotheses test?

The test statistic is given by:

[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 expected value.
  • s is the standard deviation of the sample.
  • n is the sample size.

The values of the parameters are given as follows:

[tex]\mu = 22, s = 7.043, n = 6[/tex].

The sample mean is:

[tex]\overline{x} = \frac{23 + 35 + 17 + 30 + 20 + 19}{6} = 24[/tex]

Hence the test statistic is:

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

[tex]t = \frac{24 - 22}{\frac{7.043}{\sqrt{6}}}[/tex]

t = 0.7.

More can be learned about the t-distribution at https://brainly.com/question/16194574

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