Question

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

Answer 1

Answer:

a) $\hat p_1 -\hat p_2 = 0.61-0.74 = -0.13$

A. -0.13

2) Since we are interested in the population we need to have parameters and the best option is:

D. p1 - p2

3)  $\hat p =\frac{p_1 +p_2}{2}= \frac{0.61 +0.74}{2}=0.675$

F. 0.675

4) A. p

Step-by-step explanation:

For this case we know the following info:

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"

So then we have the following proportions given:

$\hat p_1 = 0.61 , \hat p_2 =0.74$

Assuming the following questions:

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"?

$\hat p_1 -\hat p_2 = 0.61-0.74 = -0.13$

A. -0.13

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

Since we are interested in the population we need to have parameters and the best option is:

D. p1 - p2

3. If there is no difference in the population rates, which of the following must be the value of the estimate of the common population proportion of Ohio residents and Michigan residents who call a sweetened, carbonated beverage "pop"?

$\hat p =\frac{p_1 +p_2}{2}= \frac{0.61 +0.74}{2}=0.675$

F. 0.675

4. If there is no difference in the population rates, which of the following is the symbol for the estimate of the common population proportion of Ohio residents and Michigan residents who call a sweetened, carbonated beverage "pop"?

A. p