Question

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 ​respondents, 14 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 3 percentage points. What values do ModifyingAbove p with caret ​, ModifyingAbove q with caret ​, ​n, E, and p​ represent? If the confidence level is 95 ​%, what is the value of alpha ​?

Answer 1

Answer:

The value of α is 0.05.

Step-by-step explanation:

A poll of 1000 adults was conducted to determine their favorite pie.

The poll result states that among the 1000 ​respondents, 14 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 3 percentage points.

$\hat p=\text{Sample Proportion of adults who chose chocolate pie} = 0.14\\\hat q=\text{Sample Proportion of adults who did not chose chocolate pie}\\=1-\hat p\\=0.86\\n=\text{Sample size}=1000\\E=\text{Margin of Error}=0.03\\p=\text{Population Proportion of adults who chose chocolate pie}$

The confidence level is 95%.

Determine the value of significance level, α as follows:

$\text{Confidence Level}=(1-\alpha)\%\\\\95\%=(1-\alpha)\%\\\\0.95=(1-\alpha)\\\\\alpha=1-0.95\\\\\alpha=0.05$

Thus, the value of α is 0.05.