An article in the San Jose Mercury News stated that students

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

Solution

Answer to the question)

Null hypothesis; Ho: M = 4.5

Alternate hypothesis; Ha: M > 4.5

[right tailed hypothesis]

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n = 49

x bar = 5.1

s = 1.2

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test statistic formula

t = (x bar - M) / (s/sqrt(n))

t = (5.1 -4.5)/(1.2/sqrt(49))

t = 3.5

.

df = 49 - 1= 48

.

it is a right tailed test

thus p value = 0.0005 ...[used excel fromula to find it =t.dist.rt(3.5,48)]

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Inference: Since the P value 0.0005 < alpha 0.05 , we Reject the null hypothesis

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Conclusion: thus there is significant evidence to support the claim that the mean value is larger than 4.5