Q1-6BSC - Elementary Statistics

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.

Step-by-Step Solution

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 1: Given information

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

Step 2: 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.

Step 3: 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.

\({H_1}:p < 0.95\)