The website popvssoda. com collects survey data on what a person from a particular region calls a sweetened, carbonated beverage: "pop" or "soda". Northern states are known for using the word "pop", so we wish to compare the usage of "pop" for Ohio versus a more northern state, Michigan. Assuming that the data comes from a random sample, it is revealed that 61% of the sampled Ohio residents (group 1) use the word "pop" instead of "soda", and 74% of sampled Michigan residents (group 2) use the word "pop" instead of "soda". It is also revealed that more Michigan residents were surveyed than Ohio residents. You are asked to complete a hypothesis test using a 10% significance level to determine to determine if the proportion of all Ohio residents who use the word "pop" is less than that of all Michigan residents.

1. Which of the following is the value of the estimate for the difference in population proportions of Ohio residents versus Michigan residents who call a sweetened, carbonated beverage "pop"?

A. -0.13
B. 0.00
C. 0.13
D. 0.61
E. 0.643
F. 0.675
G. 0.708
H. 0.74

A. -0.13

Step-by-step explanation:

Hello!

The objective is to compare the usage of the word "pop" to refer to sweetened carbonated beverages for Ohio and Michigan.

From a random sample taken of Ohio residents, 61% of them used the word "pop" and from a random sample of Michigan residents, 74% of them used the word "pop".

You need to conduct a hypothesis test to determine if the proportion of Ohio residents that use the word "pop" is less than the proportion of Michigan residents that use the word.

Be:

X₁: Number of Ohio residents that use the word "pop" to refer to a sweetened carbonated beverage.

X₂: Number of Michigan residents that use the word "pop" to refer to a sweetened carbonated beverage.

The parameters of interest are the population proportions of both states.

Symbolized: p₁ < p₂ ⇒ you can also express it as a difference p₁ - p₂ < 0

Then the statistic hypotheses are:

H₀: p₁ - p₂ ≥ 0

H₁: p₁ - p₂ < 0

You can say then that the parameter of the test is the difference between the population proportions and its point estimate will be the difference of sample proportions, then:

Sample proportion 1 :p'₁= 0.61

Sample proportion 2: p'₂= 0.74

The difference is

p'₁ - p'₂= 0.61 - 0.74= -0.13

The correct answer is A.

I hope this helps!

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,