The$$ cross$-$tabulation data given below show the number of people who rated a customer service representative as friendly and polite based on whether the representative greeted them first. Complete parts a through d below.

$$Friendliness$/$Politeness

Staff Greeting

No

Yes

No

$13$

$3$

Yes

$15$

$21$

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Part $1$

a$.$ Write the hypotheses for the$$ chi$-$square test for independence.

Upper H $0$:

$$

Greeting and Customer Service Rating are not independent

Greeting and Customer Service Rating are dependent

Greeting and Customer Service Rating are independent

Upper H $1$:

$$

Greeting and Customer Service Rating are dependent

Greeting and Customer Service Rating are independent

Greeting and Customer Service Rating are not dependent