Question

There are 150,000 households in Market City. A local phone repair shop takes a random sample of 50 households and finds that the average number of phones per household from the sample last year that needed to be repaired was 1.05 ± 0.23. Which of the following is an estimate of the total number of phones that needed repairing last year in Market City?

Between 82 and 128 phones
Between 123,000 and 192,000 phones
Between 105 and 23 phones
Between 157,500 and 34,500 phones

Answer 1

To estimate the total number of phones needing repairs in Market City, multiply the total number of households (150,000) by the average number of repairs per household (1.05) to get 157,500 as the estimated number of repairs needed.

Step-by-step explanation:

The question asks for an estimate of the total number of phones that needed repairing last year in Market City, based on a sample survey from a local phone repair shop. To find this estimate, we can use the average number of phones that needed repair per household in our sample to estimate for the entire population of households in Market City.

We were provided with the average number of phones needing repair per household in our sample as 1.05, with a margin of error of ± 0.23. However, for the purposes of this calculation, we will consider only the point estimate of 1.05 phones per household.

To estimate the total number of phones needing repair in the entire city for last year, we multiply the number of households by the average number of repairs per household:

• Total estimated repairs = Number of households × Average repairs per household
• Total estimated repairs = 150,000 × 1.05
• Total estimated repairs = 157,500

Since we are not incorporating the margin of error into this calculation, this estimate reflects the point estimate rather than the potential range.