Question

A grocery store wants to know which system is better for decreasing the amount of time that their customers wait in checkout lines. Is there a significant difference in the average time customers wait in line using the cashier operated checkout and the self-checkout? The data was collected by recording the amount of time it takes to check out 20 customers that enter the cashier checkout line and 20 customers that enter the self-checkout line. The number of minutes from when the customer enters the checkout line completes the check out process and exits the line.

Cashier Electronic
4.21 9.66
5.55 5.9
3.02 8.02
5.13 5.79
4.77 8.73
2.34 3.82
3.54 8.01
3.2 8.35
4.5 10.49
6.1 6.68
0.38 5.64
5.12 4.08
4.26 6.71
6.19 9.91
3.79 5.47
4.25 4.06
6.32 8.65
4.45 3.5
4.26 5.58
3.46 7.41

1. Report how you analyzed the data using a two-sample t-test analysis technique

2. Include the output and any calculations of the analysis you performed on Excel (screenshot or picture).

3.. Discuss the results of your data analysis.

4. Discuss the limitation(s) of your data analysis.

5. Recommend a course of action based on your results.

Answer 1

1)

	n	Mean (μ)	Variance (SS)	Standard Deviation (SD)
Cashier	n1 = 20	μ1 = 4.242	SS1 = 1.9814	s1 = 1.4076
Electronic	n2 = 20	μ2 = 6.823	SS2 = 4.4981	s2 = 2.1209

We assume that the checkout time for cashier is less than self-checkout and check if the hypothesis is true.

The null and alternative hypotheses are
Ho :  μ1 <= μ2
Ha :  μ1 > μ2
where μ1, μ2 are the population mean checkout times for Cashier and Electronic respectively.

α = 0.05
We use independent Samples T test since population standard deviation is unknown, and sample size is small

2)

Using the following formulae, we get

Degrees of Freedom
df1 = n1 - 1 , df2 = n2 - 1 , df = n1 + n2 - 2

df = 38

Pooled Variance

Sp² = 3.2397

Mean Squared Error S_m1-m2

S_m1-m2 = 0.5692

t-statistic

t-statistic = t = -4.5345



P-value
For t = -4.5345, df = 38 we find the one tailed p-value using t tables or Excel function t.dist
p-value = 1 - t.dist(-4.5345, 38, TRUE)
p-value = 1

p-value is almost 1

3)

Decision
1 > 0.05
that is p-value is less than alpha.
Hence we DO NOT Reject Ho.

4)

Limitations

Sample size is too small

We assume the samples are from a normal population.

5)

Conclusion
There does not exist enough statistical evidence at α = 0.05 to show that cashier operated checkout takes more time than self checkout

Hence, it is not recommended to replace cashier checkout with Electronic or Self-checkout