Statistics for the Behavioral Sciences
Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781452286907
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 8, Problem 19CAP

(1)

To determine

Identify the decision for each value of p if α=0.05

  1. a) p=0.0250
  2. b) p=0.1000
  3. c) p=0.005
  4. d) p=0.0001

(1)

Expert Solution
Check Mark

Answer to Problem 19CAP

  1. a) The decision for p=0.0250 if α=0.05 is rejecting the null hypothesis.
  2. b) The decision for p=0.1000 if α=0.05 is retaining the null hypothesis.
  3. c) The decision for p=0.005 if α=0.05 is rejecting the null hypothesis.
  4. d) The decision for p=0.0001 if α=0.05 is rejecting the null hypothesis.

Explanation of Solution

Decision Rule:

If the value of p is less than α, then reject the null hypothesis.

a)

The data gives the value of p is 0.0250 and α=0.05.

The p-value is less than the value of α. That is, p(=0.0250)<α(=0.05). From the decision rule, the null hypothesis is rejected.

Hence, the decision for p=0.0250 if α=0.05 is rejecting the null hypothesis.

b)

The data gives the value of p is 0.1000 and α=0.05.

The p-value is greater than the value of α. That is, p(=0.1000)<α(=0.05). From the decision rule, fail to reject the null hypothesis.

Hence, the decision for p=0.1000 if α=0.05 is retaining the null hypothesis.

c)

The data gives the value of p is 0.005 and α=0.05.

The p-value is lesser than the value of α. That is, p(=0.005)<α(=0.05). From the decision rule, reject the null hypothesis.

Hence, the decision for p=0.005 if α=0.05 is rejecting the null hypothesis.

d)

The data gives the value of p is 0.0001 and α=0.05.

The p-value is lesser than the value of α. That is, p(=0.0001)<α(=0.05). From the decision rule, reject the null hypothesis.

Hence, the decision for p=0.0001 if α=0.05 is rejecting the null hypothesis.

(2)

To determine

Identify the decision for each value of p if α=0.01

  1. a) p=0.0250
  2. b) p=0.1000
  3. c) p=0.0050
  4. d) p=0.0001

(2)

Expert Solution
Check Mark

Answer to Problem 19CAP

  1. a) The decision for p=0.0250 if α=0.01 is retaining the null hypothesis.
  2. b) The decision for p=0.1000 if α=0.01 is retaining the null hypothesis.
  3. c) The decision for p=0.0050 if α=0.01 is rejecting the null hypothesis.
  4. d) The decision for p=0.0001 if α=0.01 is rejecting the null hypothesis.

Explanation of Solution

a)

The data gives the value of p is 0.0250 and α=0.01.

The p-value is greater than the value of α. That is, p(=0.0250)>α(=0.01). From the decision rule, fail to reject the null hypothesis.

Hence, the decision for p=0.0250 if α=0.01 is retaining the null hypothesis.

b)

The data gives the value of p is 0.1000 and α=0.01.

The p-value is greater than the value of α. That is, p(=0.1000)>α(=0.01). From the decision rule, fail to reject the null hypothesis.

Hence, the decision for p=0.1000 if α=0.01 is retaining the null hypothesis.

c)

The data gives the value of p is 0.0050 and α=0.01.

The p-value is lesser than the value of α. That is, p(=0.0050)<α(=0.01). From the decision rule, reject the null hypothesis.

Hence, the decision for p=0.0050 if α=0.01 is rejecting the null hypothesis.

d)

The data gives the value of p is 0.0001 and α=0.01.

The p-value is lesser than the value of α. That is, p(=0.0001)<α(=0.01). From the decision rule, reject the null hypothesis.

Hence, the decision for p=0.0001 if α=0.01 is rejecting the null hypothesis.

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