Consider the following competing hypotheses and accompanying sample results. Use

Question

Consider the following competing hypotheses and accompanying sample results. Use Table 2.

Calculate the value of the test statistic under the assumption that the difference is normally distributed. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

At the 5% significance level, what is the critical value? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Part B

Consider the following matched samples representing observations before and after an experiment. Assume that sample data are drawn from two normally distributed populations. Let the difference be defined as Before minus After. Use Table 2.

Construct the competing hypotheses to determine if the experiment increases the magnitude of the observations.

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Consider the following competing hypotheses and accompanying sample results. Use Table 2.

Hypotheses: H0: ?D ? 0; HA: ?D < 0 Sample results: = ?2.7, sD = 7.3, n = 20

Explanation / Answer

dbar = -2.7
sd = 7.3
n = 20

a)
Test statistic
t = (-2.7 - 0)/(7.3/sqrt(20)) = -1.6541

b)
Critical value = -1.6449

c)
Reject H0 since the value of the test statistic is less than the critical value.

Part B.

a)

H0: muD = 0; HA: muD < 0

b)

b-1.

Test statistic, t = -2.1245

b-2.

0.025 < p-value < 0.050

b-3.

Reject H0 since the p-value is less than 0.1

c)

No, Reject H0

Before After dbar 2.8 3.2 -0.4 3.1 3.4 -0.3 1.7 4.3 -2.6 -2.8 -1.7 -1.1 1.6 0.9 0.7 -1.8 1.4 -3.2 -3 -2.4 -0.6 2.9 3.2 -0.3

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