Q.39

Question

Significance tests A test of $H_{0} : p = 0.5$ versus Ha : p >0.5 has test statistic z=2.19.

(a) What conclusion would you draw at the 5 % significance level? At the 1 % level?

(b) If the alternative hypothesis were $H_{0} : p \neq 0.5$ what conclusion would you draw at the 5% significance level? At the 1 % level?

Step-by-Step Solution

Verified

Answer

a. The null hypothesis is rejected at $5 %$ significance level and not rejected at $1 %$ significance level

b. At $5 %$ and $1 %$ significance level the null hypothesis is not rejected

1Step 1: Introduction

A p-value is a factual estimation used to approve a theory against noticed information. A p-esteem estimates the likelihood of getting the noticed outcomes, it is consistent with expectations that the invalid speculation. The lower the p-esteem, the more prominent the factual meaning of the noticed distinction.

2Step 2: Explanation Part (a)

Calculating the null and alternative hypotheses,

$\begin{aligned} H_{0} : p = 0.5 \\ H_{a} : p > 0.5 \end{aligned}$

Calculating the p-value by using,

$= P (Z > | z |)$

$= P (t > | 2.19 |) = 0.0143$

The null hypothesis is rejected at $5 %$ significance level and not rejected at $1 %$ significance level as the p-value is less than $5 %$ and greater than $1 %$ .

3Step 3: Explanation Part (b)

Calculating the null and alternative hypotheses,

$\begin{aligned} H_{0} : p = 0.5 \\ H_{a} : p \neq 0.5 \end{aligned}$

The p-value is calculated as,

$= 2 \times P (Z > | Z |)$

$= 2 \times 0.014 = 0.028$

The null hypothesis is not rejected in both cases.

Q.38

Q.40