The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

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Step-by-step explanation:

a. H0: μ = 26.6

b. Ha: μ > 26.6

c. Let x = the mean age for online students at De Anza College.

d. Student’s t-distribution

e. 9.98

f. p-value = 0.0000

g. Check student’s solution.

h. i. Alpha: 0.01        

ii. Decision: Reject the null hypothesis.        

iii. Reason for decision: The p-value is less than 0.01.        

iv. There is sufficient evidence to conclude that the mean age of online students at De Anza College is greater than 26.6 years.i. (28.8, 30.0)