Question

fill in the missing values in the table. round your responses for the expected frequencies to two or more decimals responses to three or more decimal places.
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	in a church	indoors but not in a church	outdoors	total
expected frequency $f_e$	$\square$	$\square$	52.00	$\square$
$\frac{(f_o - f_e)^2}{f_e}$	$\square$	$\square$	3.250	$\square$

Explanation:

Step1: Find expected frequency sum

Total observed frequency = 260, so total expected frequency = 260.

Step2: Calculate missing expected frequencies

Let \( f_{E1} \) = In a church, \( f_{E2} \) = Indoors but not church.
\( f_{E1} + f_{E2} + 52 = 260 \) → \( f_{E1} + f_{E2} = 208 \).
Assume equal expected frequency for first two categories (common in uniform distribution): \( f_{E1} = f_{E2} = \frac{208}{2} = 104.00 \).

Step3: Compute \( \frac{(f_O - f_E)^2}{f_E} \) for first category

\( \frac{(145 - 104)^2}{104} = \frac{41^2}{104} = \frac{1681}{104} ≈ 16.163 \)

Step4: Compute \( \frac{(f_O - f_E)^2}{f_E} \) for second category

\( \frac{(76 - 104)^2}{104} = \frac{(-28)^2}{104} = \frac{784}{104} ≈ 7.538 \)

Answer:

Expected frequency (In a church): 104.00
Expected frequency (Indoors but not in a church): 104.00
\( \frac{(f_O - f_E)^2}{f_E} \) (In a church): 16.163
\( \frac{(f_O - f_E)^2}{f_E} \) (Indoors but not in a church): 7.538

(Note: Assumes uniform expected distribution; if another distribution was intended, values may vary, but uniform is standard for such problems without additional info.)