Question

In a survey of its customers, a local tire shop found that 52% of its customers are satisfied with its services and 47% are not. The sample size was 250.

A.) What percentage of customers do you believe are satisfied with this service? USe 95% confidence interval.

B.) Use 99% confidence interval and interpret your results. What would you suggestion be to the manager?

  

Answer 1

A) The 52% of the customers are satisfied with the service.

The 95% confidence interval for proportion

Given that: P=0.52,n=250,α=0.05

Lower Limit=P - Zα/2* √P*(1-P)/n

= 0.52 - 1.96*√0.52*0.48/250

= 0.52 - 1.96*0.031597

=0.52 - 0.0619

Lower Limit  =0.4581

Upper Limit=P -+Zα/2* √P*(1-P)/n

= 0.52 + 1.96*√0.52*0.48/250

= 0.52 + 1.96*0.031597

=0.52 + 0.0619

Upper Limit  =0.5819

The 95% confidence interval is (0.4581,0.5819)

B)

The 99% confidence interval for proportion

Given that: P=0.52,n=250,α=0.01

Lower Limit=P - Zα/2* √P*(1-P)/n

= 0.52 - 2.575*√0.52*0.48/250

= 0.52 - 2.575*0.031597

=0.52 - 0.0814

Lower Limit  =0.4386

Upper Limit=P +Zα/2* √P*(1-P)/n

= 0.52 + 2.575*√0.52*0.48/250

= 0.52 + 2.575*0.031597

=0.52 + 0.0814

Upper Limit  =0.6014

The 99% confidence interval is (0.4386,0.6014)

The 99% confident that the true population proportion is lies between the interval (0.4386,0.6014).