A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 11% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 99%, what is the value of alpha?

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warylucknow warylucknow · Answer 1 · 2020-05-01T10:13:01+02:00

Answer:

The value of α is 0.10.

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\times\hat q}{n}}[/tex] OR [tex]CI=\hat p\pm E[/tex]

The information provided is:

n = 500

[tex]\hat p[/tex] = 0.11

E = ± 0.05

In the (1 - α)% confidence interval for population proportion the variables are defined as follows:

[tex]\hat p[/tex] = sample proportion of people who chose chocolate pie

[tex]\hat q[/tex] = sample proportion of people who did not choose chocolate pie

n = sample selected for the poll

E = margin of error for the (1 - α)% confidence interval

p = population proportion of people who chose chocolate pie

The confidence level used is, 99%.

Compute the value of α as follows:

[tex](1-\alpha )\%=99\%\\100\%-\alpha \%=99\%\\\alpha \%=100\%-99\%\\\alpha \%=10\%\\\alpha =0.10[/tex]

Thus, the value of α is 0.10.