2The mean Verbal SAT score for the population of first students at Radford is 52

Question

2The mean Verbal SAT score for the population of first students at Radford is 520. An investigator believes that the car mean of a sample of 36 first year psychology majors is 548. The standard deviation of scores in this sample is 95. Please test the investigator's prediction using an alpha level of.05. a. Please state both the null and alternative hypotheses. b. Please write a decision rule that states when the investigator should reject the null hypothesis. c. Please show all calculations needed to generate the appropriate statistic. d. State your decision as to whether the investigator should reject the null hypothesis. e. State the conclusion the investigator is entitled to draw.

Explanation / Answer

Data:     

n = 36    

= 520    

s = 95    

x-bar = 548    

Hypotheses:     

Ho: 520    

Ha: > 520    

Decision Rule:     

= 0.05    

Degrees of freedom = 36 - 1 = 35   

Critical t- score = 1.68957244    

Reject Ho if t > 1.68957244    

Test Statistic:     

SE = s/n = 95/36 = 15.83333333   

t = (x-bar - )/SE = (548 - 520)/15.8333333333333 = 1.768421053   

p- value = 0.042853236    

Decision (in terms of the hypotheses):     

Since 1.768421053 > 1.68957244 we reject Ho and accept Ha

Conclusion (in terms of the problem):     

It appears that the mean score is greater than 520     

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