Question

In: Statistics and Probability

Testing a Claim about a Mean Test the Claim: The mean time to take this exam...

Testing a Claim about a Mean Test the Claim: The mean time to take this exam is greater than 30 minutes. (Note: There will be NO credit given for wrong answers even if they are correct based on previous wrong answers – so check your work) Sample data: n = 25, x = 32 minutes, s = 5 minutes. α = 0.05

6. What is the value of the Test Statistic? (1 Point)

7. What is/are the Critical Value(s)? (1 Point) Ho:

8. Null Hypothesis. (1 Point) H1:

9. Alternate Hypothesis. (1 Point)

10. Reject or Fail to Reject. (

Expert Solution

We want to test that mean time to take this exam is greater than 30 minutes.

Here we are going to use one sample t test because population standard deviation is unknown.

This is one sided test.

We have given Population mean µ = 30 minutes

Sample mean (x) = 32 minutes

Sample standard deviation (s) = 5 minutes

Sample size (n) = 25

Test statistics (t) = (x - µ) / (s/ √n)

t = (32 - 30)/ (5/sqrt(25))

Test statistics t = 2

The one sided t critical value at degrees of freedom n-1 = 24 and α=0.05

T_{24, 0.05} = 1.711 (from statistical table)

Rejection region: Reject H₀ if test statistics t > 1.711.

Null hypothesis H₀: µ = 30 min
Alternative hypothesis H₁: µ > 30 min

Conclusion: t statistics = 2 > t_{24, 0.05} = 1.711 that means t statistics value fall in rejection region. So we reject null hypothesis at 5% level of significance.

We can conclude that, there is sufficient evidence of 0.05 level of significance that the mean time to take this exam is greater than 30 minutes.

orchestra answered 2 years ago

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