Question

Identifying \({H_0}\) and \({H_1}\) . In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Cell Phone Claim: Fewer than 95% of adults have a cell phone. In a Marist poll of 1128 adults, 87% said that they have a cell phone.

Short answer

a.The original claim in symbolic form is written in the following manner:

\(p < 0.95\)

b. The null hypothesisand the alternative hypothesis are as follows:

\({H_0}:p = 0.95\)

\({H_1}:p < 0.95\)

Step-by-step solution

Given information

Out of 1128 adults, 87% said they have a cell phone.

Original claim

a.

It is claimed that less than 95% of adults have a cell phone;this suggests that the original claim should be that the proportion of adults who have a cell phone is less than 95% or 0.95.

Symbolically, the claim would be \(p < 0.95\), where p is the proportion of adults who have a cell phone.

Hypotheses

b.

Null hypothesis: The proportion of adults who have a cell phone is equal to 0.95.

\({H_0}:p = 0.95\)

Alternative hypothesis: The proportion of adults who have a cell phone is less than 0.95.

\({H_1}:p < 0.95\)