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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.

Short Answer

Expert verified

CI:(28.8, 30.0)

Step by step solution

01

Find H0 and Ha: We want to test if De Anza College students take less than 26.6 years old mean age for them while conducting online classes, on average.

H0:μ=26.6;Ha:μ>26.6

02

Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean age for online students at De Anza College.

Normal: N26.6,2.156

Test statistic:z=9.98

03

Calculate the p-value using the normal distribution for mean RV

p-value=0.0000

In one to two complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the mean age is 26.6), then there is a 0.0000 probability that the sample (estimated) mean age is 29.4 or more.

04

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.01Reject the null hypothesis.
p-value<0.01

Conclusion: There is sufficient evidence to conclude that the mean age of online students at De Anza College is greater than 26.6 years.

05

Confidence Interval

CI: (28.8, 30.0)

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