A 2012 study reported that the opinions of U.S.

The following information is related to questions 1-4

A 2012 study reported that the opinions of U.S. adults regarding the the issue of abortion has the following distribution:

Legal in all cases

Legal in most cases

Illegal in most cases

Illegal in all cases

Unsure

.23

.31

.23

.16

.07

700 randomly chosen U.S. adults were recently asked about their opinions regarding abortion and the data showed that:

• 154 responded that abortion should be legal in call cases
• 252 responded that abortion should be legal in most cases
• 160 responded that abortion should be illegal in most cases
• 98 responded that abortion should illegal in all cases
• 36 were unsure.

We will use the chi-square goodness-of-fit test to assess whether or not the observed data fit the distribution reported by the 2012 study.

Question 1 of 7 Points: 10

Which of the following are the correct null and alternative hypotheses in this case?

• H0: The data fit the distribution reported by the 2012 study
• Ha: The data do not fit the distribution reported by the 2012 study
• H0: The data do not fit the distribution reported by the 2012 study
• Ha: The data fit the distribution reported by the 2012 study

Question 2 of 7 Points: 10

If the distribution reported by the 2012 study is still true, how many of the 700 U.S. adults would you expect to respond that abortion should be legal in most case? In other words, what is the expected frequency of U.S. adults who respond that abortion should be legal in most case?

31

252

160

217

161

Question 3 of 7 Points: 10

The chi-square goodness-of-fit test statistic in this case is X

2

=12.02

X2

12.02

.

Using the chi-square table (linked here), what can you say about the p-value of the test?

0.01 < p-value < 0.02

p-value > 0.1

0.02 < p-value < 0.05

0.05 < p-value < 0.1

p-value < 0.01

Question 4 of 7 Points: 10

Which of the following is the correct conclusion at the 0.05 significance level in this case?

We do not have evidence to conclude that the data do not fit the distribution reported by 2012. study.

We have evidence to conclude that the data do not fit the distribution reported by 2012 study.

The following information is related to questions 5-7

A company has released its new phone which is available in 4 capacity models: 32GB, 64GB, 128GB, and 256GB. A store has sold 284 phones over the last week: 63 phones of the 32GB model, 73 phones of the 64GB model, 77 of the 128GB model, and 71 of the 256GB model. We will use the chi-square goodness-of-fit test to asses whether the four models’ total sales are significantly different from one another.

Question 5 of 7 Points: 10

Which of the following are the correct null and alternative hypotheses in this case?

• H0: Sales are consistent with the claim of equal demand for the four models
• Ha: Sales are not consistent with the claim of equal demand for the four models
• H0: Sales are not consistent with the claim of equal demand for the four models
• Ha: Sales are consistent with the claim of equal demand for the four models

Question 6 of 7 Points: 10

If the null hypothesis is correct, how many phones (out of 284 phones that were sold) would you expect to be sold from the 32GB, 64GB, 128GB, 256GB models, respectively? In other words, what are the expected frequencies in this case?

25, 25, 25, 25

32, 64, 128, 256

63, 73, 77, 71

71, 71, 71, 71

284, 284, 284, 284

Question 7 of 7 Points: 10

If we would like to carry out the test at a significance level (threshold) of 0.05, which of the following is critical value that we need to compare the test statistic to? Use the chi-square distribution linked here.

7.815

11.070

9.488

11.345