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$0.65,0.30,0.05$.

Short answer

Assumption $1$is satisfied and Assumption $2$is not satisfied.

Step-by-step solution

Step 1. Given information 

Sample size$n=50$.

Step 2. Assumption 1:

Relative Frequency $p$	Expected frequency $np$
$0.65$	$32.5$
$0.30$	$15$
$0.05$	$2.5$

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 $5=\frac{1}{3}\times 100$

$=33.333333>20\%$

$\therefore$Assumption $2$ is not satisfied.