New_Packaging

Last updated: 22:05:19 IST, 05 January, 2024

Decision Scenario

A firm wants to assess if 65% of its customers are preferring a new packaging that they introduced. When they contacted 100 randomly selected customers and checked, they found that 66 of them preferred the new packaging (Case 1).

What if they found that 70 of them preferred the new packaging? (Case 2)

What if they found that 74 of them preferred the new packaging? (Case 3)

Solution Approach

• Single population proportion
• Ho: p \(\leq\) 0.65
• Ha: p \(>\) 0.65}

Case 1: 66 of 100 people preferred the new packaging

prop_test_res <- prop.test(66,100,alternative = 'greater',p=0.65)
prop_test_res

## 
##  1-sample proportions test with continuity correction
## 
## data:  66 out of 100, null probability 0.65
## X-squared = 0.010989, df = 1, p-value = 0.4583
## alternative hypothesis: true p is greater than 0.65
## 95 percent confidence interval:
##  0.5736545 1.0000000
## sample estimates:
##    p 
## 0.66

Case 2: 70 of 100 people preferred the new packaging

prop_test_res <- prop.test(70,100,alternative = 'greater',p=0.65)
prop_test_res

## 
##  1-sample proportions test with continuity correction
## 
## data:  70 out of 100, null probability 0.65
## X-squared = 0.89011, df = 1, p-value = 0.1727
## alternative hypothesis: true p is greater than 0.65
## 95 percent confidence interval:
##  0.6149607 1.0000000
## sample estimates:
##   p 
## 0.7

Case 3: 74 of 100 people preferred the new packaging

prop_test_res <- prop.test(74,100,alternative = 'greater',p=0.65)
prop_test_res

## 
##  1-sample proportions test with continuity correction
## 
## data:  74 out of 100, null probability 0.65
## X-squared = 3.1758, df = 1, p-value = 0.03737
## alternative hypothesis: true p is greater than 0.65
## 95 percent confidence interval:
##  0.6569121 1.0000000
## sample estimates:
##    p 
## 0.74