paraphrase----1 page....1.5hrs deadline
The major shopping areas in the community of Springdale include Springdale Mall, West Mall,
and the downtown area on Main Street. A telephone survey has been conducted to identify
strengths and weaknesses of these areas and to find out how they fit into the shopping activities
of local residents. The 150 respondents were also asked to provide information about themselves
and their shopping habits. The data are provided in the file Shopping (attached below). The
variables in the survey can be found in the file Coding (attached below).
In this exercise, some of the estimation techniques presented in the module will be applied to the
Springfield Shopping survey results. You may assume that these respondents represent a simple
random sample of all potential respondents within the community, and that the population is
large enough that application of the finite population correction would not make an appreciable
difference in the results.
Managers associated with shopping areas like these find it useful to have point estimates
regarding variables describing the characteristics and behaviors of their customers. In addition, it
is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the
benefit of the techniques presented in this module and applied here.
1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement.
1. Determine the point estimate, and then construct the 95% confidence interval for μ7 = the average attitude toward Springdale Mall.
2. Repeat part (a) for μ8 and μ9, the average attitudes toward Downtown and West Mall, respectively.
2. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate and then construct the 95% confidence interval for p26 = the population proportion of males.
3. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate and then construct the 95% confidence interval for p28 = the population proportion in the “single or other” category.
4. Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each. If the managers want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample size be for each mall?
1.The point estimate and the 95% confidence interval for μ7 = the average attitude toward Springdale Mall is
The point estimate x
x n
standard deviation
2
1
x x SD
n
The 95% confidence interval for mean average attitude is 0.05/ 2, 1n
SD x t
n
Count 150
Average 3.813
Standard deviation 1.064
Standard error 0.087
t-significant value at 5% 1.976
Point estimate 3.813
95% Lower limit 3.642
95% upper limit 3.985 2. The point estimate and the 95% confidence interval for μ8 = the average attitude toward Down town Mall is
The point estimate x
x n
standard deviation
2
1
x x SD
n
The 95% confidence interval for mean average attitude is 0.05/ 2, 1n SD
x t n
Count 150
Average 3.407
Standard deviation 1.124
Standard error 0.092
t-significant value at 5% 1.976
Point estimate 3.407
95% Lower limit 3.225
95% upperlimit 3.588 3. The point estimate and the 95% confidence interval for μ9 = the average attitude toward West Mall is
The point estimate x
x n
standard deviation
2
1
x x SD
n
The 95% confidence interval for mean average attitude is 0.05/ 2, 1n SD
x t n
Count 150
Average 3.287
Standard deviation 1.183
Standard error 0.097
t-significant value at 5% 1.976
Point estimate 3.287
95% Lower limit 3.096
95% upper limit 3.478 II The point estimate and the 95% confidence interval for p26 = the population proportion of males is
Point estimate No.of Males
p n
95% confidence interval for population proportion of males is
0.05/2
1p p p Z
n
Count 150
No.of Males 64
No.of Females 86
Proportion of Males 0.427
Z value at 0.05/2 level 1.960
Standard error 0.040
Point estimate 0.427
95% confidence interval lower limit 0.348
95% confidence interval upper limit 0.506 III The point estimate and the 95% confidence interval for p28 = the population proportion in the “single or other” category is
Point estimate No.of single or other
p n
95% confidence interval for population proportion single or other is
0.05/2
1p p p Z
n
Count 150
NO. of Single or other 83
No.of Married 67
Proportion of single or other 0.553
Z value at 0.05/2 level 1.960
Standard error 0.041
Point estimate 0.553
95% confidence interval lower limit 0.474
95% confidence interval upper limit 0.633 IV. The estimated sample sizes for each of the sample with the margin of error 0.05 with 95% confidence is
2
0.05/ 2 *
Sample size Z SD
ME
SPRINGDALE DOWN TOWN WEST
Margin of error 0.05 0.05 0.05
Standard deviation 1.064 1.124 1.183
Z-value at 0.05/2 level 1.96 1.96 1.96
Sample size 1741 1941 2152