Question

The accompanying data represent the total travel tax​ (in dollars) for a​ 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts​ (a) through​ (c) below.

68.43

78.73

69.41

84.89

79.03

87.78

101.73

98.75

​(a) Determine a point estimate for the population mean travel tax.

A point estimate for the population mean travel tax is ​$___ (Round to two decimal places as​ needed.)

​(b) Construct and interpret a 95​% confidence interval for the mean tax paid for a​ three-day business trip.

Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

A. The travel is between $___ and $___ for ___% of all cities.

B. One can be ___% confident that the all cities have a travel tax between $___ and $___.

C. There is a ___% probability that the mean travel tax for all cities is between $___ and $___.

D. One can be ___% confident that the mean travel tax for all cities is between $___ and $___.

​(c) What would you recommend to a researcher who wants to increase the precision of the​ interval, but does not have access to additional​ data?

The researcher could decrease the sample standard deviation.

A. The researcher could decrease the sample standard deviation.

B. The researcher could increase the sample mean.

C. The researcher could increase the level of confidence.

D. The researcher could decrease the level of confidence.

Answer 1

The accompanying data represent the total travel tax​ (in dollars) for a​ 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers.

a)

A point estimate for the population mean travel tax is sample mean of travel tax

Sr.No.	X	(X-M)	(X-M)^2
1	68.43	-15.16	229.83
2	78.73	-4.86	23.62
3	69.41	-14.18	201.07
4	84.89	1.3	1.69
5	79.03	-4.56	20.79
6	87.78	4.19	17.56
7	101.73	18.14	329.06
8	98.75	15.16	229.83
Total	668.75	0.03	1053.44
M=Total / 15	83.59

c)

If we want to increase precision:

1. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
2. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
3. Use a one-sided confidence interval. ...
4. Lower the confidence level.

Answer:- D. The researcher could decrease the level of confidence.