Question

Formulating the null and Alternative Hypothesis: Are US people taller in 2018 than in 1920?

1 point possible (graded)

As in a previous problem, you try to answer the question "Were people in the U.S. taller in 2018 than in 1920, when the average height was 5.5 feet?" by sampling 1 million individuals labeled 1,2,…,106 randomly from the 2018 U.S. population.

You take as the status quo that the people are not taller in 2018, and look for evidence in the data to reject this status quo. In other words, you assume people are not taller in 2018, until “proven" otherwise.

You model the height of the i-th individual as a random variable Xi and make the assumption, based on 1920 data, that X1,…,Xn∼iidN(μ,1.3) where μ is an unknown parameter.

You rephrase the question of interest as: Is μ>5.5? or is μ≤5.5?

Formulate the null and alternate hypothesis for this test. Which of the following depicts Θ0 and Θ1?

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Answer 1

The appropriate null and Alternative Hypothesis are,

where are the true mean heights of US people in 2018 and 1920 respectively.

The null and alternate hypothesis for the test when we know the true mean heights of US people in 1920 is 5.5

Θ0 = 5.5

Θ1 ~ N(μ,1.3) where μ>5.5