Question

Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidant in foods such as blueberries can reduce and even reverse those age-related declines, at least in laboratory rats (Joseph,et al.,1999). Based on these results, one might theorize that the same antioxidants might benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives and gives each participant a daily dose of blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce a mean score of M = 50.2. For the general population of elderly adults scores on the test average LaTeX: \muμ =45 and form a normal distribution with a LaTeX: \sigmaσ = 9. Can the researchers conclude that the supplement significantly increases cognitive skills? Use a one-tail (not two-tail) test with LaTeX: \alphaα= .05. Please answer the question using all of the steps presented on your practice problem assignment. (null in word, alternative in words, null in symbols, alternative in symbols, critical region z, all steps in the analysis computing your computed z, make a decision, and give a conclusion. Do not skip around in the steps. Provide steps in an orderly steps by step manner.

Answer 1

Null hypothesis: The population mean of elderly adult score on the test is equal to 45

Alternative hypothesis: The population mean of elderly adult scores on the test is greater than 45

H​​​​​​0: = 45

H1: > 45

At alpha = 0.05, the critical value is z0.05 = 1.645

Reject H0, if z > 1.645

The test statistic is

Since the test statistic value is greater than the critical value (2.31 > 1.645), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that the supplement significantly increases cognitive skills.