You\'re writing an article for Consumer Reports, based on a survey of the magazi

Question

You're writing an article for Consumer Reports, based on a survey of the magazine's readers. on the reliability of various household appliances. A total of 1,338 readers said they had Maytag washing machines, and 294 of these people reported at least one episode in the last year in which they the 480 people who said they owned a General Electric (GE) washer reported one or more repair calls in the same period had to call for someone to come and repair the machine. Only 192 of (a) Person A says "There were 294 people with one or more repair episodes for the Maytag machines and only 192 for GE, so GE machines are more reliable." Person B objects to this argument, noting that "(1338 - 294) 1044 readers reported no problems with their Maytag washers, versus only (480-192) - 288 trouble-free reports for GE, so Maytag mach is incorrect, compute a fair num and compare. (This is not a trick question.) ines are better." Briefly explain why both of these people's reasoning erical summary of the reliability of these two brands (b) Intuitively, which of these two reliability estimates (GE or Maytag) is likely to be more accurate? (That is, assuming that the Maytag and GE samples were representatively the populations of all people owning those brands of washing machine, drawn from which estimate should have the smaller amount of uncertainty attached to it as an ucated guess for the corresponding population quantity?) Explain briefly

Explanation / Answer

Among the surveyed, a total of 1338 had Maytag washing machines and 480 people said that they owned a GE washer.

the sample size of the Maytag owners is much higher than the sample size of the GE owners. This means it is not appropriate to compare these two samples based on numbers. Hence to compare 284 of the 1338 Maytag owners reported repair episodes with 192 out of 480 GE owners, is not approriate as the number of repondents is different for each of the brands. Similarly to say that 1044 Maytag owners reported no issues compared to 288 GE owners and hence Maytag is better is also not correct as the number of respondents is different in each case.

The correct method is to compare the proportion of each brand who have reported a repair epsiode.

the proportion of Maytag owners who reported one or more repair epsiodes = 294/1338 = 0.22

the proportion of GE owners who reported one or more repair epsiodes = 192/480 = 0.40

That means a higher proportion of GE owners have reported at least one repair episode compared to MAytag owners.

Hence we can say that Maytag washers are more reliable than GE washers

b) The sample size of Maytag owners is 1338. The sample size of GE owners is 480. We know the opinion of more number of Maytag owners copared to GE owners. Assuming that the population of Maytag and GE owners are very big compared to the sample sizes, we can say that we have higher representation of Maytag population compared to the GE population. A larger sample size always reduces the error in estimating the population parameters.

Hence we can say that the reliability estimate (estimate of the proportions that we did in part a) of Maytag is likely to be more accurate than the GE estimates.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.