Question

State the null and the alternative hypothesis for the above scenario

Answer 1

We were given:

X = 61% = 0.61

P = 65% = 0.65 =μ

n = 900

α = 0.05

let us first get the value of Z

Recall,

`z=\frac{x-\mu}{\sqrt[]{(P(1-P))/(n)}}`

On substitution

`\begin{gathered} z=\frac{0.61-0.65}{\sqrt{(0.64-(1-0.64))/(900)}} \\ \\ z=-2.5 \end{gathered}`

z = -2.5

Let us get the probability at z = -2.5

From the table:

P = 0.0062

Since the probability calculated is bigger than ).05 the given probability, then the company's claim is not true

Also,

Null Hypothesis states that:

`H_o:P\ge0.64`

While,

Alternative Hypothesis states thus:

`H_o:P<0.64`