Question

Chapter 8 hand-in Homework
Pat I
A random sample of 15 customers’ waiting time in a bank was selected, giving the following results in minutes:

0.38
2.34
3.02
3.2
3.54
3.79
4.21
4.5
4.77
5.1
5.13
5.55
6.1
6.19
6.46

1) Based on the sample above, what is the point estimate of the true percentage (same as True Population) of customers’ waiting time in a bank?  
2) To estimate the true percentage of customers’ waiting time in a bank, how large a sample must be taken to insure the estimate is off by no more than + 2% with 99% certainty?  

3) What would happen to the sample size above if the error was increased to 4%?  

4) What would happen to the sample size in question 2 above if the error was decreased to 1%?  
Part II
A bottle of water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottle is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon.

Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.

b) On the basis of these results, do you think that the distributor has a right to complaint to the water bottling company? Why?

c) Must you assume that the population amount of water per bottle is normally distributed? Explain.

Part III
In a survey of 529 travelers, 386 said that location was very important and 323 said that room quality was very important in choosing a hotel.
a) Construct a 95% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel.
b) The percentage of travelers that said that location was very important for choosing a hotel is a statistic or a parameter? Explain
c) If we need to conduct a follow up study, what sample size is need to estimate the population proportion of travelers who said that location was very important for choosing a hotel with 95% confidence within ± 5%?

 

Answer 1

From the given data: n = 529

number of travelers who said location is more important = x = 386

proportion of travelers who said location is more important:

Confidence level = 95%

a) 95% confidence interval formula for population proportion:

Plugging in values we get,

Hence 95% confidence interval for the population proportion of travelers who said that location was very important for choosing a hotel is (0.6919, 0.7675)

b) Percentage of travelers who said location was very important is 72.97%. It is a statistic.

Because this value is obtained from a sample of size 529 travelers. Thus this value describes sample. On other hand parameter describes whole population. Here no true population proportion is known. Therefore percentage of travelers saying location was very important is a statistic.

c) We have margin of error of 5%

i.e. ME = 0.05

Sample size formula:

Plug in values:

Hence revised sample size would be 304 in order to get 5% error for 95% confidence interval.