Question

EXCEL CAN BE USED

You still work at that Starbucks. Due to COVID-19, the business is slow. As the manager, you had to ask two employees of yours to stay home and wait for more shifts to open. Meanwhile, you are bored. So you look into historical data from the store and dig out the following:

Customers spent an average of $4.18 on iced coffee with a standard deviation of $0.84.

43% of iced-coffee customers were women.

21% were teenage girls.

In order to increase sales, Starbucks start to offer a half-priced Frappuccino beverage between 3 pm and 5 pm for a limited time. One month after the marketing period ends, you survey 50 of your iced-coffee customers and find that:

They spent an average of $4.26 on the drink.  

46% were women.

34% were teenage girls.

Since these numbers are different from what the store historical data has told, you wonder whether the store data are outdated.  

1. What's the probability that customers spend an average of $4.26 or more on iced coffee? Round your answer to four decimal places. Based on this probability, are you convinced that the store data on the average spend on the drink are outdated? Hint: If the probability is < 0.05, the store data are outdated.  

2. What's the probability that 46% or more of iced-coffee customers are women? Round your answer to four decimal places. Based on this probability, are you convinced that the store data on women are outdated? Hint: If the probability is < 0.05, the store data are outdated.  

3. What's the probability that 34% or more of iced-coffee customers are teenage girls? Round your answer to eight decimal places. Based on this probability, are you convinced that the store data on teenage girls are outdated? Hint: If the probability is < 0.05, the store data are outdated.  

Answer 1

1)

Population mean, =$4.18

Population standard deviation, =$0.84

Sample size, n =50

Sample mean, =$4.26

Z = =(4.26 - 4.18)/(0.84/​​​​​​) =0.6734

The probability that customers spend an average of $4.26 or more on iced coffee =P(X 4.26) =P(Z 0.6734) =0.2503

Since the probability of 0.2503 > 0.05, the store data are not outdated.

2)

Population proportion of women, p =0.43

Sample proportion, =0.46

Standard Error, SE = = =0.070014

Z =( - p)/SE =(0.46 - 0.43)/0.070014 =0.4285

The probability that 46% or more of iced-coffee customers are women =P(X 0.46) =P(Z 0.4285) =0.3341

Since the probability of 0.3341 > 0.05, the store data are not outdated.

3)

Population proportion of teenage girls, p =0.21

Sample proportion, =0.34

Standard Error, SE = =0.057602

Z =(0.34 - 0.21)/0.057602 =2.2569

The probability that 34% or more of iced-coffee customers are teenage girls =P(X 0.34) =P(Z 2.2569) =0.012

Since the probability of 0.012 < 0.05, the store data are outdated.