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Sladkaya [172]
3 years ago
7

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd =

0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
x 28 31 20 25 28 27 33 35
y 26 27 26 25 29 32 33 34
Mathematics
1 answer:
swat323 years ago
6 0

Answer:

Test statistic, t_{s} = -0.603 (to 3 dp)

Step-by-step explanation:

Deviation, d = x -y

Sample mean for the deviation

\bar{d} = \frac{\sum x-y}{n}

\bar{d} = \frac{(28-6) + (31-27)+(20-26)+(25-25)+(28-29)+(27-32)+(33-33)+(35-34)}{8} \\\bar{d} = -0.625

Standard deviation: SD = \sqrt{\frac{\sum d^{2} - n \bar{d}^2}{n-1}  }

\sum d^{2}  = (28-26)^2 + (31-27)^2 +(20-26)^2 +(25-25)^2 +(28-29)^2 +(27-32)^2 +(33-33)^2 +(35-34)^2\\\sum d^{2}  = 63

SD = \sqrt{\frac{63 - 8 *  (-0.625)^2}{8-1}  }

SD =2.93

Under the null hypothesis, the formula for the test statistics will be given by:

t_{s} = \frac{ \bar{d}}{s_{d}/\sqrt{n}  } \\t_{s} = \frac{- 0.625}{2.93/\sqrt{8}  }

t_{s} = -0.6033

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