Finding Mean and Standard Deviation of a Sample

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Calculate the mean of the sampling distribution of p̂.

• μ_p̂ = 0.20

• μ_p̂ = 20

• μ_p̂ = 4

• μ_p̂ = 0.05

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Calculate the standard deviation of the sampling distribution of p̂.

• σ_p̂ = 8.9

• σ_p̂ = 0.089

• σ_p̂ = 0.20

• σ_p̂ = 1.789

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Interpret the standard deviation of the sampling distribution of p̂, σ_p̂ = 0.089.

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 0.20.

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.20 from the true proportion of p = 0.089.

• In SRSs of size n = 0.20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 20.

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 20.

In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district. Let p̂ = the proportion of Democrats in the sample. Calculate the mean of the sampling distribution of p̂.

• μ_p̂ = 0.55

• μ_p̂ = 55

• μ_p̂ = 275

• μ_p̂ = 0.275

In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district. Let p̂ = the proportion of Democrats in the sample. Calculate the standard deviation of the sampling distribution of p̂.

• σ_p̂ = 2.2

• σ_p̂ = 0.022

• σ_p̂ = 0.55

• σ_p̂ = 11.124

In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district. Let p̂ = the proportion of Democrats in the sample. Interpret the standard deviation of the sampling distribution of p̂, σ_p̂ = 0.022.

• In SRSs of size n = 500, the sample proportion of Democrats will typically vary by about 0.022 from the true proportion of p = 0.55.

• In SRSs of size n = 500, the sample proportion of Democrats will typically vary by about 0.55 from the true proportion of p = 0.022.

• In SRSs of size n = 500, the sample proportion of Democrats will typically vary by about 2.2 from the true proportion of p = 5.5.

• In SRSs of size n = 55, the sample proportion of Democrats will typically vary by about 0.022 from the true proportion of p = 500.