Does it make sense? For exercises 5-8, decide whether the statement makes sense

Question

Does it make sense? For exercises 5-8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these statements have a definitive answer, so your explanation is more important than your chosen answer. 5. Larger Sample Size. Two different surveys will be conducted to estimate the mean salary of employees who have taken a statistics course. If the first survey has a larger sample size than the second survey, the first survey will result in a sample mean that is closer to the proportion mean (when compared with the second survey). The reason this is true is because the first survey had a larger sample size. 6. Larger sample size. When a random sample is used to estimate, a population mean, the sample mean tends to become a better estimate of the population mean as the sample size increases. 7. Large Sample Size A researcher for a car dealership wants to estimate the mean age of cars in hs county. He goes to the largest shopping mall, he randomly selects 3000 cars in the parking lot, and he obtains their ages from the registration stickers on the car windows. He then computes the mean age of the sample of 3,000 cars. The sample mean is a good estimate of the population mean because the large sample size compensates for the fact that he is using a convenience sample. 8. Survey. In an Adecco Staffing survey of 1000 adults in the U.S. 140 (14%) said that salary was the most important feature of their job. The sample proportion of 0.14 cannot be a good estimate of the population proportion because this survey is based on such a small proportion of the populat

Explanation / Answer

Answer to question# 5)

This statement is correct , because as the sample size increases, more of the true population gets covered under the study and thus the larger sample has mean that estimates the true population mean more appropriately as compared to a smaller sample

.

Answer to question# 6)

Ths statement is true. As the sample size increases the standard error of the sample decreases, thus providing a better estimate of the true population

Standard error = standard deviation/ sample size

So if the size increases, the standard error decreases

if the standard error decreases, thus the estimate is more accurate

Thus sample mean tends to population mean

.

Answer to question# 7)

This is not true

The sample mean can be a good estimate only when it covers the population completely. In this scenario the population is not covered completely , only a segment of it has been included in the sample. Such a sample will surely provide biased estiamtes. It is important that the population be covered completely in all aspects.

.

Answer to part 8)

The statement is false.

Explanation: Since the sample size 1000 is large enough , definitely this sample proportion of 0.14 is a good estimate of the population proportion. For a sample to be large the sample size must be 30 or above. Since 1000 is a very large sample size, definitely it provides us a better estimate of the population proportion

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

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