A researcher wishes to estimate the number of days it takes an automobile dealer to sell...

A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Nissan Sentra. A sample of 50 cars has a mean time on the dealer’s lot of 70 days. Assume the standard deviation for the population is 7.5 days

A) Find the best point estimate of the population mean. ___________(hint: no work needed)

B) Find the 95% confidence interval of the population mean.

Conclusion: We can say with 95% confidence that the population mean is between __________and ____________ days.

Solutions

Expert Solution

Solution :

Given that,

= 70

= 7.5

n = 50

At 99% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

a) Margin of error (E) = Z_/2* ( / $\sqrt$ n)

= 1.96 * (7.5/ $\sqrt$ 50)

E = 2.08

b) At 95% confidence interval estimate of the population mean is,

- E < < + E

70 - 2.08 < < 70 + 2.08

67.92 < < 72.08

We can say with 95% confidence that the population mean is between 67.92 and 72.08 days.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

. A researcher wishes to see if the mean number of days that a basic, low-price,...

. A researcher wishes to see if the mean number of days that a basic, low-price, small automobile sits on a dealer’s lot is 29. A sample of 30 automobile dealers has a mean of 30.1 days for this type of automobile. At an alpha 0f 0.05, test the claim that the meantime is greater than 29 days. The standard deviation (sigma) of the population is 3.8 days. a. Support the claim b. Do not support the claim

A researcher wishes to estimate the number of households with two computers. How large a sample...

A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 4%? A previous study indicates that the proportion of households with two computers is 25%.

A researcher wishes to estimate the number of households with two computers. How large a sample...

A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two computers is 24%

Location is known to affect the number, of a particular item, sold by an automobile dealer....

Location is known to affect the number, of a particular item, sold by an automobile dealer. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 18 days and location B was observed for 13 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 49 of these...

A researcher at a major hospital wishes to estimate the proportion of the adult population of...

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed to be 90% confident that the sample proportion will not differ from the true proportion by more than 5% A. If no preliminary estimate is available B. If a recent survey indicated that 43% of the population suffers from high blood pressure.

A researcher wishes to? estimate, with 99 ?% ?confidence, the population proportion of adults who are...

A researcher wishes to? estimate, with 99 ?% ?confidence, the population proportion of adults who are confident with their? country's banking system. His estimate must be accurate within 2 ?% of the population proportion. ?(a) No preliminary estimate is available. Find the minimum sample size needed. ?(b) Find the minimum sample size? needed, using a prior study that found that 36 ?% of the respondents said they are confident with their? country's banking system. ?(c) Compare the results from parts...

2) A researcher wishes to be 95% confident that her estimate of the true proportion of...

2) A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 2% of the true proportion. Find the sample size necessary if: a) No estimate of the sample proportion is available. b) In a prior study a sample of 190 individuals showed that 23 traveled overseas last year.

A researcher for a car insurance company wishes to estimate themean annual premium that men...

A researcher for a car insurance company wishes to estimate the mean annual premium that men aged 20-24 years pay for their car insurance. A random sample of 50 men aged 20-24 years shows a mean of $711. Assume that the distribution of annual premiums has a standard deviation of $185.a) Find a 94% confidence interval for the mean annual premium for all men aged 20-24 years.b) What is the error of the estimate?c) Find the 99% confidence interval for...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think the...

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 4% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they think their president can control the price of gasoline. c) Compare...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident...

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 4% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 34% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b)....

Subjects