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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To  evaluate  the  success  of  a  1-year  experimental  program  designed  to  increase  the  mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year’s  statewide  average  of  525  for  underprivileged  seniors.  The  researchers  want  to  determine  whether the experimental program has increased the mean achievement level over the previous year’s statewide average. If alpha=.05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, sigma=80.
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