Question

In each case, decide whether Assumptions $1$and $2$for using chi-square goodness-of-fit test are satisfied.

Sample size:$n=50$.

Relative frequencies:$0.20,0.20,0.25,0.30,0.05$.

Short answer

Both Assumption$1$and$2$are satisfied.

Step-by-step solution

Step 1. Given information

Sample size$n=50$.

Step 2. Assumption 1:

Relative frequency $p$	Expected frequency $np$
$0.20$	$10$
$0.20$	$10$
$0.25$	$12.5$
$0.30$	$15$
$0.05$	$2.5$

All expected frequencies are $\ge 1$.

$\therefore$Assumption$1$is satisfied.

Step 3. Assumption 2.

Number of expected frequencies less than $5=1$

Percentage of expected frequencies less than $5=\frac{1}{5}\times 100$

$=20$

$\therefore$Assumption $2$ is satisfied.