Question

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

Sample size: $n=100$.

Relative frequencies:$0.65,0.30,0.05$.

Short answer

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

Step-by-step solution

Step 1. Given information

Sample size$n=100$.

Step 2. Assumption 1:

Relative frequency $p$	Expected frequency $np$
$0.65$	$65$
$0.30$	$30$
$0.05$	$5$

All the expected frequencies are$\ge 1$.

$\therefore$Assumption $1$is satisfied.

Step 3. Assumption 2:

Number of expected frequencies less than $5=0$

$\%$of expected frequencies less than $5=\frac{0}{3}\times 100$

$=0.0<20\%$

$\therefore$Assumption $2$is satisfied.