Question

Note: I've reordered which proportion is considered  p¯p¯ 1 and which is  p¯p¯ 2 so we get a...

Note: I've reordered which proportion is considered  p¯p¯ 1 and which is  p¯p¯ 2 so we get a positive difference between the proportions.

Consider the following competing hypotheses and accompanying sample data. Note I've rewritten the question so you have a positive difference. Use Table 1.
H0: p1 − p2 < 0
HA: p1 − p2 > 0
  x1 = 275 x2 = 250
  n1 = 400 n2 = 400
a.

At the 5% significance level, find the critical value(s). Remember, we are not pooling.  (Round final answer to 2 decimal places.)
  Critical value   
b.

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  Test statistic   
c. What is the conclusion?

  • Reject H0 since the value of the test statistic is not less than the critical value.

  • Do not reject H0 since the value of the test statistic is not less than the critical value.

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

  • Do not reject H0 since the value of the test statistic is less than the critical value.
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The statistical software output for this problem is:

Hence,

a) Critical value = -1.65

b) Test statistic = 1.86

c) Reject H0 since the value of the test statistic is not less than the critical value.

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