Question

A security expert claims that exactly 19​% of all homeowners have a home security alarm. State Upper H 0 and Upper H Subscript a in words and in symbols. Then determine whether the hypothesis test for this claim is​ left-tailed, right-tailed, or​ two-tailed. Explain your reasoning.

Answer 1

Answer: Null hypothesis : $H_0: p=0.19$

Alternative hypothesis : $H_a: p\neq0.19$

The test is two-tailed test.

Explanation:

A null hypothesis $(H_0)$ is defined as

• hypothesis that proposes that there is no difference between particular characteristics of a population.
• It takes ' = ', ' ≤' , '≥'

Alternative hypothesis $(H_a)$ is defined as

• hypothesis that proposes that there is a significant difference between particular characteristics of a population.
• It takes ' ≠ ', ' <' , '>'

• If alternative hypothesis is two tailed then we apply two tail test and  if alternative hypothesis is left tailed/ right tailed then we apply two left -tailed / right tailed test respectively.

Let p be the proportion of all homeowners have a home security alarm.

As per given, A security expert claims that exactly 19​% of all homeowners have a home security alarm.

i.e.  Null hypothesis : $H_0: p=0.19$

Alternative hypothesis : $H_a: p\neq0.19$

Here , the alternative hypothesis is two-tailed.

Therefore, the test is two-tailed test.