Question

question 2 of 7 (1 point) | question attempt: 1 of unlimited
part 1 of 6
(a) what is the point estimate?
the point estimate is 120.1.
part 2 of 6
(b) find the critical value.
the critical value is 1.96.
part 3 of 6
(c) find the standard error. round to four decimal places.
the standard error is 3.1113.
part: 3 / 6
part 4 of 6
(d) find the margin of error. round to two decimal places.
the margin of error is .

Explanation:

Step1: Recall Margin of Error Formula

The margin of error (E) for a confidence interval (when using z - critical value) is given by the formula \( E = z_{\alpha/2}\times SE \), where \( z_{\alpha/2} \) is the critical value and \( SE \) is the standard error.

Step2: Substitute the Values

We know that the critical value \( z_{\alpha/2}=1.96 \) and the standard error \( SE = 3.1113 \).
Substitute these values into the formula: \( E=1.96\times3.1113 \).
Calculate \( 1.96\times3.1113 = 6.098148 \).

Step3: Round to Two Decimal Places

Rounding \( 6.098148 \) to two decimal places, we look at the third decimal place which is 8. Since \( 8\gt5 \), we round up the second decimal place. So \( 6.098148\approx6.10 \).

Answer:

6.10