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Statistics - Memory Booster

Statistics - Memory Booster

  • 31st Aug, 2021
  • 16:42 PM

Question:

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. To test whether this herbal mixture improves
memory, a researcher obtains a sample of 16 people and has each person take the suggested dosage
each day for a month. At the end of the month, each individual takes an internet-based memory test.
The scores from the sample produced a mean of 25 with a standard deviation of 8. In the general
population, the internet test is known to have a mean of 20.
(a) Address this problem using the six steps of hypothesis testing. (14 points) (b) Given the results of
this experiment, what sort of statistical error could have occurred? (2 points) (c) If appropriate, calculate
effect size. (3 points) (d) Calculate the 95% confidence interval for the sample mean (4 points) (e)
Another researcher claims that the dependent variable in this study has poor construct validity. What
are they referring to?

Answer:

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. To test whether this herbal mixture improves
memory, a researcher obtains a sample of 16 people and has each person take the suggested dosage
each day for a month. At the end of the month, each individual takes an internet-based memory test.
The scores from the sample produced a mean of 25 with a standard deviation of 8. In the general
population, the internet test is known to have a mean of 20.
(a) Address this problem using the six steps of hypothesis testing. (14 points)
Sample Size = 16
Sample Mean = 25
Sample SD = 8
Population Mean = 20
This problem can be solved using the t test for a single sample
Null hypothesis: Mean score on the internet-based memory test of individuals who take the herbal
mixture is lesser than or equal to the population score of individuals on the memory test
Alternate hypothesis: Mean score on the internet-based memory test of individuals who take the herbal
mixture is higher than the population score of individuals on the memory test
Significance level = 5%

We compute the t-statistic = (25-20)/(8/SQRT(16)) = (5)/(8/4) = 2.50
Degrees of freedom = Sample Size – 1 = 15
P-value = 0.012259
Thus, at 5% significance level, we reject the null hypothesis. Thus, average score on the internet-based
memory test of individuals who take the herbal mixture is higher than the population score of
individuals on the memory test
(b) Given the results of this experiment, what sort of statistical error could have occurred? (2 points)
Measurement errors, construct validity errors, measurement validity errors, sampling errors etc could
have taken place.
(c) If appropriate, calculate effect size. (3 points)
Effect size = (25-20)/8 = 0.625
(d) Calculate the 95% confidence interval for the sample mean (4 points)

95% confidence interval is equal to 25 ± 2.13145*(8/SQRT(16)) = 25 ± 2.13145*2 = 25 ± 4.262899
95% confidence interval = [20.7371, 29.2629]
(e) Another researcher claims that the dependent variable in this study has poor construct validity. What
are they referring to?
Construct validity refers to the validity of results obtained from the test measurements. The researcher
may claim that the internet-based memory test may not accurately measure the memory of a person.

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