an article in the magazine knitters united states that a random sampling of subscribers found that 75 out of 120 people surveyed knitted exclusively with wool yarn. The article concludes that, with a 95% confidence level, the true proportion of their subscribers who knit exclusively with wool yarn is between 53.8% and 71.1%
Using z= 1.960, evaluate the conclusion of the report
A. The conclusion of the article is not accurate because the 95% confidence interval is (48.4%,76.6%), which incldes values outside of the interval (53.8%, 71.1%)
B The conclusion of the article is not accurate because the 95% confidence interval is (52.2%, 72.8%). which includes values outside of the interval (53.8%,71.1%)
C. The conclusion of the article is accurate because the 95% confidence interval is (53.8%,71.1%)
D. The conclusion of the article is partially accurate because the 95% confidence interval is (55.3%,69.7%), which lies within the interval (53.8%, 71.1%)
To evaluate the conclusion, we need to compare the given 95% confidence interval with the provided interval of (53.8%, 71.1%).
The given confidence interval is (48.4%, 76.6%), which means that, with a 95% confidence level, the true proportion of subscribers who knit exclusively with wool yarn could be between 48.4% and 76.6%.
Comparing this with the interval (53.8%, 71.1%), we can see that the given interval includes values outside of this range. Specifically, the lower bound of 48.4% is lower than the lower bound of 53.8% in the provided interval. Therefore, we can conclude that option A is correct:
A. The conclusion of the article is not accurate because the 95% confidence interval is (48.4%, 76.6%), which includes values outside of the interval (53.8%, 71.1%)