Although there is a popular belief that herbal remedies such as Ginkgo biloba an

Question

Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research. In a typical study, a researcher obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test are normally distributed with a mean of = 80 and a standard deviation of = 21. The sample of research participants had an average of M = 83.

(a) In a sentence, state the null hypothesis being tested.

The herbal supplements have no effect on memory scores.

The herbal supplements have an increasing effect on memory scores.    

The herbal supplements have a decreasing effect on memory scores.

(c) Conduct the hypothesis test using a two-tailed test with = 0.05. (Round your answers to two decimal places.)

z-critical = +-

z=

Conclusion

Fail to reject the null hypothesis. The herbal supplements do not have a significant effect on memory scores.

Reject the null hypothesis. The herbal supplements have a significant effect on memory scores.    

Fail to reject the null hypothesis. The herbal supplements have a significant effect on memory scores.

Reject the null hypothesis. The herbal supplements do not have a significant effect on memory scores.

Explanation / Answer

a)

OPTION A: The herbal supplements have no effect on memory scores. [ANSWER]

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c)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   80  
Ha:    u   =/   80  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.96 [ANSWER]

**************************
              
Getting the test statistic, as              
              
X = sample mean =    83          
uo = hypothesized mean =    80          
n = sample size =    16          
s = standard deviation =    21          
              
Thus, z = (X - uo) * sqrt(n) / s =    0.571428571 = 0.57 [ANSWER]

****************************          
              
As |z| < 1.96, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence,

OPTION A: Fail to reject the null hypothesis. The herbal supplements do not have a significant effect on memory scores. [ANSWER]

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