Question

In: Statistics and Probability

Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following...

Consider the following hypothesis test.

H0: μd ≤ 0

Ha: μd > 0

(a)

The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.)

Element Population Difference
1 2
1 21 18
2 28 25
3 18 16
4 20 19
5 26 25

(b)

Compute

d.

(c)

Compute the standard deviation

sd.

Conduct a hypothesis test using

α = 0.05.

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Solutions

Expert Solution

a)

                         Population

Element           1                   2                         Difference

1                     21               18                              3

2                     28               25                              3

3                     18               16                              2

4               20 19    1      

5                     26               25                              1

b) = (3 + 3 + 2 + 1 + 1)/5 = 2

c) sd = sqrt(((3 - 2)^2 + (3 - 2)^2 + (2 - 2)^2 + (1 - 2)^2 + (1 - 2)^2)/4) = 1

The test statistic is

  

P-value = P(T > 4.472)

             = 1 - P(T < 4.472)

            = 1 - 0.9945

            = 0.0055

Since the P-value is less than , so we should reject the null hypothesis.


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