Chi Square GOF

In a recent survey of members of the American Association of Retired Persons (AARP), 9% of members stated they had attained less than a high school diploma, 26% were high school graduates, 32% had some college, and 33% possessed at least a 4-year degree. An administrator at a local retirement home wonders if this distribution is true for his residents. He takes a random sample of 300 residents and finds 41 have less than a high school diploma, 86 have high school diplomas, 98 had some college and 75 had at least a 4-year degree.

State the hypotheses that the administrator is interested in testing.

• Ho: The distribution of education at the retirement home is not the same as the stated distribution from the AARP.

  Ha: The distribution of education at the retirement home is the same as the stated distribution from the AARP.

• Ho: The distribution of education at the retirement home is the same as the stated distribution from the AARP.

  Ha: The distribution of education at the retirement home is not the same as the stated distribution from the AARP.

• Ho: The distribution of education at the retirement home is the same as the stated distribution from the AARP.

  Ha: The distribution of education at the retirement home is greater than the stated distribution from the AARP.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.B.5

In a recent survey of members of the American Association of Retired Persons (AARP), 9% of members stated they had attained less than a high school diploma, 26% were high school graduates, 32% had some college, and 33% possessed at least a 4-year degree. An administrator at a local retirement home wonders if this distribution is true for his residents. He takes a random sample of 300 residents and finds 41 have less than a high school diploma, 86 have high school diplomas, 98 had some college and 75 had at least a 4-year degree.

Calculate the expected count for a test of the null hypothesis.

• Less than high school diploma: = 78

  High school graduate: = 96

  Some college: = 27

  At least a 4-year degree: = 99

• Less than high school diploma: = 27

  High school graduate: = 78

  Some college: = 131

  At least a 4-year degree: = 151

• Less than high school diploma: = 27

  High school graduate: = 78

  Some college: = 96

  At least a 4-year degree: = 99

Tags

CCSS.HSS.MD.A.2

In a recent survey of members of the American Association of Retired Persons (AARP), 9% of members stated they had attained less than a high school diploma, 26% were high school graduates, 32% had some college, and 33% possessed at least a 4-year degree. An administrator at a local retirement home wonders if this distribution is true for his residents. He takes a random sample of 300 residents and finds 41 have less than a high school diploma, 86 have high school diplomas, 98 had some college and 75 had at least a 4-year degree.

Calculate the value of the chi-square test statistic for these data.

• 13.94

• 20.43

• 11.89

• 17.17

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.B.5

A certain candy company claims that their multi-colored candies are equally distributed. The candies come in 5 flavors: lemon, orange, lime, strawberry and grape. To test this claim, Jenna bought a randomly selected bag of the candies and counted the flavors of the candies in her sample: 7 lemon, 5 orange, 6 lime, 4 strawberry, and 2 grape.

What is Jenna’s sample size?

• 12

• 16

• 20

• 24

Tags

CCSS.6.SP.B.5A

A certain candy company claims that their multi-colored candies are equally distributed. The candies come in 5 flavors: lemon, orange, lime, strawberry and grape. To test this claim, Jenna bought a randomly selected bag of the candies and counted the flavors of the candies in her sample: 7 lemon, 5 orange, 6 lime, 4 strawberry, and 2 grape.

Check if the conditions for performing a chi-square test for goodness of fit are met.

• Yes, all conditions have been met

• No, the sampling wasn't random

• No, the Large Counts Condition is not satisfied (all expected values are greater than 5)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

4. According to the U.S. Census, the age distribution for the U.S. population in 2000 is given below, along with a random sample of 1200 residents of Massachusetts taken in 2000. The table displays the sample data.

What would appropriate hypotheses be?

• Ho: The Massachusetts age distribution is the same as the national distribution.

  Ha: The Massachusetts age distribution is not the same as the national distribution.

• Ho: The Massachusetts age distribution is not the same as the national distribution.

  Ha: The Massachusetts age distribution is the same as the national distribution.

• Ho: The Massachusetts age distribution is the same as the national distribution.

  Ha: The Massachusetts age distribution is greater than the national distribution.

• Ho: The Massachusetts age distribution is the same as the national distribution.

  Ha: The Massachusetts age distribution is less than the national distribution.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.B.5

CCSS.HSS.ID.A.2

According to the U.S. Census, the age distribution for the U.S. population in 2000 is given below, along with a random sample of 1200 residents of Massachusetts taken in 2000. The table displays the sample data.

Have all conditions be satisfied to do a Chi-Square GOF Test?

• No, Large Counts Condition not met.

• No, sampling was not random.

• Yes, all conditions met.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

According to the U.S. Census, the age distribution for the U.S. population in 2000 is given below, along with a random sample of 1200 residents of Massachusetts taken in 2000. The table displays the sample data.

What is the 𝑋², P-value, and df?

• 𝑋²: 5.32

  P-value: .066

  df:3

• 𝑋²: 5.32

  P-value: .191

  df:3

• 𝑋²: 6.11

  P-value: .066

  df:4

• 𝑋²: 6.11

  P-value: .191

  df:4

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

. According to the U.S. Census, the age distribution for the U.S. population in 2000 is given below, along with a random sample of 1200 residents of Massachusetts taken in 2000. The table displays the sample data.

Is there convincing evidence that the age distribution of Massachusetts is different from the U.S. age distribution? Use a 5% level of significance.

• Because the P-value is less than .05, we reject Ho. There is convincing evidence that the Massachusetts age distribution differs from the national distribution.

• Because the P-value is greater than .05, we reject Ho. There is not convincing evidence that the Massachusetts age distribution differs from the national distribution.

• Because the P-value is less than .05, we fail to reject Ho. There is convincing evidence that the Massachusetts age distribution differs from the national distribution.

• Because the P-value is greater than .05, we fail to reject Ho. There is not convincing evidence that the Massachusetts age distribution differs from the national distribution.

Tags

CCSS.HSS.IC.B.4