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"Phillip鈥檚 Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, 鈥淣o way!鈥�

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It鈥檚 all just for fun.

C鈥檓on please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, 鈥淚 think it鈥檚 much less.

We must do a hypothesis test.

And if you are right,

I won鈥檛 put up a fight.

But, if not, then my case will rest.鈥�

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they鈥檇 occasionally buy.

Then there鈥檚 the other thirty-one,

Who said they鈥檇 never have this done.

So now this poem鈥檚 finished.

Will his hopes be diminished,

Or will my nephew have his fun?

Step by step solution

01

Given information

Philip told his mother that half of his friends have pierced their ears, but his mother replied that it is less than half. Out of$50$friends$19$have pierced their ears.

02

Explanation

State the hypothesis:

The null hypothesis states that half of the friends of Philip have pierced their ears and the alternate hypothesis states that less than half of the friends of Philip have pierced their ears.

$$\begin{gathered} H_0:p=0.50 \\ {H}_0:p<0.50 \end{gathered}$$

The normal distribution is:

$N\left(0.50,\sqrt{\frac{\left(0.50\right)\left(0.50\right)}{50}}\right)$

The Z test statistic is calculated as:

$z=\frac{p^{鈭�}-p}{\sqrt{{\displaystyle \frac{p\left(1-p\right)}{n}}}}$

Where n is the sample size of $50$respondents:

$$\begin{gathered} p^{鈭�}=\frac{x}{n} \\ =\frac{19}{50} \\ =0.38 \end{gathered}$$

Substitute the $p^{鈭�}$value in the Z test statistic:

$$\begin{gathered} z=\frac{p^{鈭�}-p}{\sqrt{{\displaystyle \frac{p\left(1-p\right)}{n}}}} \\ =\frac{0.38-0.50}{\sqrt{{\displaystyle \frac{p\left(1-p\right)}{n}}}} \\ =\frac{-0.12}{0.0707} \\ =-1.697 \end{gathered}$$

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