Hypothesis Testing: an Example

Hypothesis Testing: an Example

<p> One-Sample t-Test – Example 2 (Memory Booster) ANSWER KEY</p><p>A nutrition store in the mall is selling “Memory Booster,” which is a concoction of herbs and minerals that is intended to improve memory performance, but there is no good reason to think it couldn't possibly do the opposite. To test the effectiveness of the herbal mix, a researcher obtains a sample of 8 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of μ = 7.</p><p>Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Two-tailed b. Hypotheses in words Alternative hypothesis: Those who take Memory Booster will have a significantly different memory score from that of the general population.</p><p>Null hypothesis: Those who take Memory Booster will have the same memory score as that of the general population. c. Statistical hypotheses</p><p>HA: µMB ≠ 7</p><p>H0: µMB  7</p><p>Step 2. Set the significance level   = .05 Determine tcrit. ± 2.365</p><p>Step 3. Compute the appropriate statistical test.</p><p>Memory Squared 2 after taking X Deviation Deviation 2  X  X  8 8 2 s     1.143 Memory X  X ( X  X ) n 1 8 1 7 Booster (X) 8 8 0 0 9 8 1 1 6 8 -2 4 8 8 0 0 9 8 1 1 8 8 0 0 s2 1.143 7 8 -1 1 X sX    .143  0.378 9 8 1 1 n 8</p><p>∑X = 64 SS = ∑ ( X  X ) 2 = N= 8 8 X = 8 X   8  7 1 tobt     2.65 s X 0.378 0.378 Step 4. Make a decision. Determine whether the value of the test statistic is in the critical region. Draw a picture. Label tcrit and tobt. Is tobt in the critical region? __yes____ Should you reject or retain the H0? reject </p><p> tcrit = -2.365 tcrit = +2.365 tobt = 2.65</p><p>Step 5. Report the statistical results.</p><p> t(7) = 2.65, p < .05.</p><p>Step 6. Write a conclusion. </p><p>People who took Memory Booster had significantly higher memory scores (M = 8) than the general population (µ = 7). </p><p>Step 7. Compute the estimated d. X   8  7 1 estimated d     .94 s X 1.143 1.069</p><p>Step 8. Compute r2 and write a conclusion. 2.652 7.023 7.023 r 2     .5008 2.652  7 7.023  7 14.023</p><p>Approximately 50% of the variance in scores on the memory test can be attributed to Memory Booster. or</p><p>Taking Memory Booster accounts for 50.08% of the variance in scores on the memory test.</p>

View Full Text

Details

  • File Type
    pdf
  • Upload Time
    -
  • Content Languages
    English
  • Upload User
    Anonymous/Not logged-in
  • File Pages
    2 Page
  • File Size
    -

Download

Channel Download Status
Express Download Enable

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

  • Not to be reproduced or distributed without explicit permission.
  • Not used for commercial purposes outside of approved use cases.
  • Not used to infringe on the rights of the original creators.
  • If you believe any content infringes your copyright, please contact us immediately.

Support

For help with questions, suggestions, or problems, please contact us