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A psychologist wants to know whether memory performance is reduced by old age. She randomly selects 67 elderly individuals and finds that their mean score on a standardized memory test equals 514. Scores on the standardized memory test in the general population are distributed normally with a mean equal to 600 and a standard deviation equal to 112. Is there sufficient evidence at the 0.1 significance level to conclude that memory performance is reduced by old age

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Answer:


z=(514-600)/((112)/(√(67)))=-6.285

The p value for this case is given by:


p_v =P(z<-6.285)=1.64x10^(-10)

Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age

Explanation:

Information given


\bar X=514 represent the sample mean for the scores on a standardized memory


\sigma=112 represent the population standard deviation


n=67 sample size


\mu_o =600 represent the value that we want to verify


\alpha=0.1 represent the significance level

z would represent the statistic


p_v represent the p value

System of hypothesis

We want to check if the true mean for this case is less than 600, the system of hypothesis would be:

Null hypothesis:
\mu \geq 600

Alternative hypothesis:
\mu < 600

Since we know the population deviation the statistic for this case is given by:


z=(\bar X-\mu_o)/((\sigma)/(√(n))) (1)

Replacing the info given we got:


z=(514-600)/((112)/(√(67)))=-6.285

The p value for this case is given by:


p_v =P(z<-6.285)=1.64x10^(-10)

Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age

User Richie Li
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