High School

June is a researcher. She read a 2016 study that published the following population distribution for Americans:

**Age Group and Percentage:**
- 0-18: 24%
- 19-25: 9%
- 26-34: 12%
- 35-54: 26%
- 55-64: 13%
- 65+: 15%

She wonders if these figures still hold true, so she takes a sample of 38 Americans and records their ages. Here are the results:

**Age Group and Observed Counts:**
- 0-18: 9
- 19-25: 3
- 26-34: 5
- 35-54: 10
- 55-64: 5
- 65+: 6

June wants to use these results to carry out a [tex]\chi^2[/tex] (chi-squared) goodness-of-fit test to determine if her sample disagrees with the official percentages.

Which count(s) make this sample fail the large counts condition for this test?

Answer :

Based on the results of June's research, the counts that fail the large counts condition are:

  • The expected count of the 19-25 age group.
  • The expected count of the 26-34 age group.
  • The expected count of the 55-64 age group.

Why do these groups fail the large counts condition?

The large counts condition is that the expected value of each observed category should be at least 5.

Expected values of each age group can be found by multiplying the percentage found in the 2016 study by the sample size in the sample June took.

Age group Percentage Expected value (38 x percentage)

0 - 18 24% 9.12

19 - 25 9% 3.42

26 - 34 12% 4.56

35 - 54 26% 9.88

55 - 64 13% 4.94

65+ 15% 5.7

The expected values less than 5 are 19 - 25, 26 - 34, and 55 - 64.

Find out more on the sampling conditions at https://brainly.com/question/1601772.

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