Question

When it comes to technology’s influence on America’s young adults, reading is not dead-at least not the news. Overall, more Americans prefer to watch their news than to read it or listen to it. But does that preference vary by age? To explore this question, we took a large random sample of young American adults (18-34 years old) and a large random sample of older American adults (50+ years old) and asked each if they prefer to watch the news versus reading the news. Using the sample results, we constructed a 99% confidence interval for the difference in the population proportion of young American adults who prefer to watch the news versus reading the news less the population proportion of older American adults who prefer to watch the news versus reading the news to be between (-0.005, 0.258).

Question 2 Subquestions

2.a

1 point(s)

Select the option that best completes the following interpretation statement:

We estimate the values of the difference in the ________________ proportions vary by roughly

_______________ from the difference in the ________________ proportions, on average.

population, 0.1315, sample

population, 0.0510, sample

population, 0.1265, sample

sample, 0.1315,population

sample, 0.0510, population

sample, 0.1265, population

2.b

1 point(s)

Correct or Incorrect : If we repeated this procedure many times and for each repetition we computed the 99% confidence interval, we would expect 99% of the resulting intervals to contain the difference in the sample proportion of young American adults who prefer watching the news to reading the news less the sample proportion of older American adults who prefer watching the news to reading the news.

Correct

Incorrect

2.c

1 point(s)

Correct or Incorrect: If we were to use the same data and test the hypotheses H0: p1 = p2 versus Ha: p1 ≠ p2, we would fail to reject the null hypothesis at the 1% signficance level.

Correct

Incorrect

2.d

1 point(s)

Correct or Incorrect: Because most of the reasonable values in the 99% confidence interval are positive, we can say that the population proportion of young American adults who prefer watching the news to reading the news is significantly higher than the population proportion of older American adults who prefer watching the news to reading the news.

Correct

Incorrect

2.e

1 point(s)

Correct or Incorrect : We estimate the difference in the population proportion of young American adults who prefer to watch the news versus reading the news less the population proportion of older American adults who prefer to watch the news versus reading the news to be 12.65% with a 99% margin of error of 13.15%

Correct

Incorrect

2.f

1 point(s)

Correct or Incorrect: With 99% confidence, we estimate that the population proportion of young American adults who prefer to watch the news versus reading the news is between 0.5% below and 25.8% above the population proportion of older American adults who prefer to watch the news versus reading the news.

Correct

Incorrect

Answer 1

a) Margin of error = (0.258 - (-0.005))/2 = (0.258 + 0.005)/2 = 0.1315

= 0.258 - 0.1315 = 0.1265

We estimate the values of the difference in the population proportion vary by roughly 0.1265 from the difference in the sample proportion, on average.

Option - C is correct.

b) option - a) Correct

c) Since the confidence interval contains the hypothesized value 0, so we should not reject the null hypothesis.

Option - A) correct

d) Option - B) incorrect

Since the confidence interval contains both positive and negative values so there is no significant difference between the two population proportions.

E) Option - A) correct

Margin of error = (0.258 - (-0.005))/2 = (0.258 + 0.005)/2 = 0.1315

= 0.258 - 0.1315 = 0.1265

F) Option - A) incorrect.

With 99% confidence , we estimate that the population proportions of young American adults who prefer to watch the news versus reading the news is between 0.5% and 25.8%.