Question

а)

Using the following 95% confidence interval for the true mean number of Pringles in a single Pringles canister, which of the following is the best interpretation?

98 < µ < 102

Group of answer choices

We are 95% sure the true mean Pringles per canister is between 98 Pringle chips and 102 Pringle chips.

We are 95% sure the true mean Pringles per canister is between 98 Pringle chips and 100 Pringle chips.

We are 95% sure the true mean Pringles per canister is between 100 Pringle chips and 102 Pringle chips.

b)

A dog researcher wants to estimate what proportion of Americans want to marry their dog. How many Americans must be sampled in order to estimate the true proportion to within 3% at the 95% confidence level?

Group of answer choices

n = 752

n = 1068

Cannot determine because no estimate of p or q exists in this problem

n = 4269

n = 30

c)

Star Magazine reports that celebrity Twitter accounts have an average of 2 million followers. Blogger Perez Hilton believes that the true average number of Twitter followers for celebrities is significantly different from that. Perez randomly samples 44 celebrities on Twitter and calculates an average of 3 million followers. Which of the following set of hypotheses is correct to test Perez Hilton’s claim?

Group of answer choices

H0: µ = 2 million vs. Ha: µ ≠ 2 million

H0: µ ≤ 2 million vs. Ha: µ > 2 million

H0: µ ≤ 3 million vs. Ha: µ > 3 million

H0: µ ≤ 2 million vs. Ha: µ > 3 million

Answer 1

a)
We are 95% sure the true mean Pringles per canister is between 98 Pringle chips and 102 Pringle chips.

b)
Option B, 1068

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.96/0.03)^2
n = 1067.11

Therefore, the sample size needed to satisfy the condition n >= 1067.11 and it must be an integer number, we conclude that the minimum required sample size is n = 1068
Ans : Sample size, n = 1068

c)
H0: µ = 2 million vs. Ha: µ ≠ 2 million