Justify a claim about a population proportion by comparing the claimed value with the interval of plausible values from the sample.
A survey conducted by a national research center asked a random sample of 920 teenagers in the United States how often they use a video streaming service. From the sample, 59% answered that they use a video streaming service every day.
Based on the confidence interval in part (a), do the sample data provide convincing statistical evidence that the proportion of all teenagers in the United States who would respond that they use a video streaming service every day is not 0.5 ? Justify your answer.
The 95% confidence interval of (0.558, 0.622) indicates that any value between 0.558 and 0.622 is a plausible value for the proportion of all teenagers in the United States who use video streaming every day. Because the value 0.5 is not contained in the interval, the sample data provide convincing statistical evidence that the proportion of all teenagers in the United States who would use a streaming service every day is not 0.5.
Scoring:
Essentially correct (E) if the response provides both:
1. A correct conclusion that there is convincing evidence, consistent with the interval calculated in part (a).
2. Correct justification based on whether 0.5 is contained in the interval calculated in part (a).
Partially correct (P) if the response satisfies only one of the two components.
Incorrect (I) if the response does not meet the criteria for E or P.