10.1 Practice

A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch.

State appropriate hypotheses for performing a test of the company’s claim.

(LT 10.1.1 #1)

• H₀: The distribution of type of nuts in this batch is the same as the claimed distribution.

  H_a: The distribution of type of nuts in this batch is not the same as the claimed distribution.

• H₀: The distribution of type of nuts in this batch is not the same as the claimed distribution.

  H_a: The distribution of type of nuts in this batch is the same as the claimed distribution.

• H₀: p_cashews = 0.27, p_almonds = 0.52, p_macadamia = 0.13, p_brazil = 0.08

  H_a: At least 2 of the proportions are wrong.

• H₀: p_cashews = 0.52, p_almonds = 0.27

  H_a: , p_macadamia = 0.13, p_brazil = 0.08

Kellogg’s Froot Loops® cereal comes in 6 colors: orange, yellow, purple, red, blue, and green. Are these colors uniformly distributed? Charise poured out her morning bowl of cereal and methodically counted the number of cereal pieces of each color.

State appropriate hypotheses for testing if the proportion of each color of Froot Loops is the same.

(LT 10.1.1 #2)

• H₀: The colors of Kellogg’s Froot Loops are uniformly distributed.

  H_a: The colors of Kellogg’s Froot Loops are not uniformly distributed.

• H₀: The colors of Kellogg’s Froot Loops are not uniformly distributed.

  H_a: The colors of Kellogg’s Froot Loops are uniformly distributed.

• H₀: p_blue = p_orange = p_yellow = p_purple = p_red = p_green = 20

  H_a: At least 2 of the proportions are different

• H₀: p_blue = p_orange = p_yellow = 0.20

  H_a: p_purple = p_red = p_green = 0.20

A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch.

H₀: The distribution of type of nuts in this batch is the same as the claimed distribution.

Calculate the expected counts for a test of the null hypothesis stated. Select all the expected counts.

(LT 10.1.2 #1)

• almond: 40.5

• cashew: 83

• macadamia: 19.5

• brazil : 12

• cashew: 78

Kellogg’s Froot Loops® cereal comes in 6 colors: orange, yellow, purple, red, blue, and green. Are these colors uniformly distributed? Charise poured out her morning bowl of cereal and methodically counted the number of cereal pieces of each color.

H₀: The colors of Kellogg’s Froot Loops are uniformly distributed.

Calculate the expected counts for a test of the null hypothesis stated.

(LT 10.1.2 #2)

• The expected count for each color is 20.

• orange = 28, yellow = 21, purple = 16, red = 25, blue = 14, green = 16

• orange = 20, yellow = 20, purple = 10, red = 20, blue = 10, green = 10

• You can't calculate it!

A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch.

Expected Count:

Cashew: 78, Almond: 40.5, Macadamia: 19.5, Brazil: 12

Calculate the value of the χ² test statistic.

(LT 10.1.3 #1)

• χ² = 6.60

• χ² = 0.0858

• χ² = 3

• χ² = unknown

Kellogg’s Froot Loops® cereal comes in 6 colors: orange, yellow, purple, red, blue, and green. Are these colors uniformly distributed? Charise poured out her morning bowl of cereal and methodically counted the number of cereal pieces of each color.

Expected Counts:

orange = 20, yellow = 20, purple = 20, red = 20, blue = 20, green = 20

Calculate the value of the χ² test statistic.

(LT 10.1.3 #2)

• χ² = 7.9

• χ² = 0.1618

• χ² = 5

• χ² = 0.0953