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MMLU / A farmer who raises hens for egg production wants his eggs to have a mean mass…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A farmer who raises hens for egg production wants his eggs to have a mean mass of 56 grams. He is considering the purchase of a different type of hen, so he took a random sample of 18 eggs laid by this type of hen. The distribution of the masses is symmetric and mound-shaped with a mean of 54.1 grams and no outliers. The farmer conducted a t-test to see if there is evidence that the eggs from these hens have a mean mass that is different from 56 g and got a test statistic of t= -1.973. If he uses a 5% significance level, which is the correct conclusion and reason?

choices

  1. Because tis more extreme than ±1.96, he should reject the null hypothesis. He has convincing evidence at the 5% significance level that the mean mass of eggs from these hens is different from 56 grams.
  2. Because tis less extreme than the critical value of t for 17 degrees of freedom, he should not reject the null hypothesis. He does not have convincing evidence at the 5% significance level that the mean mass of eggs from these hens is different from 56 grams.
  3. Because tis less extreme than the critical value of t for 18 degrees of freedom, he should not reject the null hypothesis. He does not have convincing evidence at the 5% significance level that the mean mass of eggs from these hens is different from 56 grams.
  4. Because tis more extreme than the critical value of t for 18 degrees of freedom, he should reject the null hypothesis. He has convincing evidence at the 5% significance level that the mean mass of eggs from these hens is different from 56 grams.

subject

high_school_statistics

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Source and history

task_id
f234c7f3-1012-55d3-be2e-2d9c6c0f8eed
task_key
all--test--f234c7f3-1012-55d3-be2e-2d9c6c0f8eed
task_revision_id
1
config / split
all / test

Official source

initial import