91Ó°ÊÓ

The null hypothesis is a typical statistical hypothesis which recommends that no statistical relationship and significance exists in a bunch of given single noticed variables, between two arrangements of noticed information and estimated peculiarities.

In random order, two cups were presented to the people. some people drank fresh coffee first and some drank instant coffee.

Hence people have taken the coffee in random order.

The sample size is n =$50$

People that chose fresh coffee x = $36$

role="math" localid="1652930402772" $\stackrel{-}{p}=\frac{x}{n}=\frac{36}{50}=0.72$

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.5\\ H_a:p>0.5\end{array}$

Random selection of people from a sample of $50$,

role="math" localid="1652930469566" $n{p}_0=50×0.5=25$

$\begin{array}{r}n{p}_0â‰\yen 10\end{array}$

$n\left(1−p_0\right)=50×(1−0.5)=25$

$n\left(1−p_0\right)â‰\yen 10$

using,

$Z=\frac{\stackrel{-}{p}−p_0}{\sqrt{\frac{P_0\left(1−p_0\right)}{n}}}$

$$\begin{gathered} Z=\frac{0.72−0.50}{\sqrt{\frac{0.5(1−0.5)}{50}}} \\ =\frac{0.22}{0.0707} \\ =3.11 \end{gathered}$$

The p-value is $3.11$

Now, considering $P(Z<3.11)=0.9991$

$$\begin{gathered} P(Z=3.11)=1−P(Z<3.11) \\ =1−0.9991=0.0009 \end{gathered}$$

Hence we can say that coffee drinkers favour fresh-brewed coffee from the above evidence.