Math533 Poject B 1 
Ottmas Richards
Project B
Professor Heard
Statistics 533
A manager at AJ Davis department store has speculated on certain customer statistics in hopes to get a better understanding of his target market, thus improving revenue though marketing and sales initiatives. His first assumption is that the average annual income of 50 randomly selected customers is less than $50,000. After calculating the data this assumption proved to be true, as we can say with 95% certainty that the income is less than $47,510. The next assumption is that more than 40% of his customers live in urban areas. After computing the data, we cannot be certain this is accurate. The data falls too close for me to be confident in this assumption; the 95% confidence interval is too wide. The third assumption is that the average number of years the customers have lived at their current home is less than 13 years. Again, this was an accurate assumption as we can say with a high degree of confidence than most customers have lived at their current location for less than 13 years as the mean was found to be 12.38 years. Finally, the manager assumed the average mean credit balance for suburban customers is greater than $4300. This was found to be an accurate assumption. The 95% lower confidence limit was found to be greater than $4300.
a) The average (mean) annual income was less than $50,000
Null Hypothesis: The average annual income was greater than or equal to $50,000
Ho:u = 50,000
Alternative Hypotheiss: The average annual income was less than $50,000
Ha:u <50,000
Test Statistic:
Rejection Region: For a=.05, one sided Z-test, Z<-1.645
Assumptions:
-Sample is randomly selected
-Sample is large (z ≥ 30)
-Central Limit Theorem applies, test statistic will be approximately normal
One-Sample Z
Test of mu = 50 vs < 50 (in $1,000’s)
The assumed standard deviation = 14.55
95% Upper N Mean SE Mean Bound Z P 95% CI
50 43.48 2.06
Project B
Professor Heard
Statistics 533
A manager at AJ Davis department store has speculated on certain customer statistics in hopes to get a better understanding of his target market, thus improving revenue though marketing and sales initiatives. His first assumption is that the average annual income of 50 randomly selected customers is less than $50,000. After calculating the data this assumption proved to be true, as we can say with 95% certainty that the income is less than $47,510. The next assumption is that more than 40% of his customers live in urban areas. After computing the data, we cannot be certain this is accurate. The data falls too close for me to be confident in this assumption; the 95% confidence interval is too wide. The third assumption is that the average number of years the customers have lived at their current home is less than 13 years. Again, this was an accurate assumption as we can say with a high degree of confidence than most customers have lived at their current location for less than 13 years as the mean was found to be 12.38 years. Finally, the manager assumed the average mean credit balance for suburban customers is greater than $4300. This was found to be an accurate assumption. The 95% lower confidence limit was found to be greater than $4300.
a) The average (mean) annual income was less than $50,000
Null Hypothesis: The average annual income was greater than or equal to $50,000
Ho:u = 50,000
Alternative Hypotheiss: The average annual income was less than $50,000
Ha:u <50,000
Test Statistic:
Rejection Region: For a=.05, one sided Z-test, Z<-1.645
Assumptions:
-Sample is randomly selected
-Sample is large (z ≥ 30)
-Central Limit Theorem applies, test statistic will be approximately normal
One-Sample Z
Test of mu = 50 vs < 50 (in $1,000’s)
The assumed standard deviation = 14.55
95% Upper N Mean SE Mean Bound Z P 95% CI
50 43.48 2.06