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alexandr1967 [171]
3 years ago
12

Suppose we have a set of paired data, and let d = xafter − xbefore . The null hypothesis is H0 : μd = 0, the alternative hypothe

sis is Ha : μd ≠ 0, and the population standard deviation σ is not known. Jordan collects a sample of size n = 9 and computes d¯= 2.2 and sd = 3.3A) What is the value of the test statistic?B) The probability of obtaining a test statistic greater than Jordan's test statistic is 0.0403. Use this probability to determine the P-value for Jordan's hypothesis test. (Round to three decimal places.)
Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

(a) The value of the test statistic is, <em>t</em> = 2.

(b) The <em>p</em>-value of the test is 0.081.

Step-by-step explanation:

The hypothesis for the paired difference test is:

H₀: \mu_{d}=0 vs. Hₐ: \mu_{d}\neq 0

<u>Given</u>:

\bar d=2.2\\SD_{d}=3.3\\n=9

(a)

The test statistic is:

t=\frac{\bar d}{\frac{SD_{d}}{\sqrt{n}} } \\=\frac{2.2}{\frac{3.3}{\sqrt{9}} }\\=2

The value of the test statistic is, <em>t</em> = 2.

(b)

It is provided that the P(T>2)=0.0403.

But the hypothesis test is two-tailed.

The <em>p</em>-value for the two-tailed test is:

p-value=2P(t>2) or p-value=2P(t

The <em>p</em>-value is:

p-value=2P(t>2)=2\times0.0403=0.0806\approx0.081

Thus, the <em>p</em>-value of the test is 0.081.

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