Do good smells bring good business? Businesses know that customers often respond

Question

Do good smells bring good business? Businesses know that customers often respond to background music. Do they also respond to stimulating odors such as lemon? One study of this question took place in a pizza restaurant in France on two Saturday evenings in May. The two evenings were chosen so they were comparable in many ways such as weather and customer count, so the evenings were considered to be two independent random samples from spring Saturday evenings at this restaurant. On one evening, a lemon scent was spread through the restaurant. On the other evening, no scent was used. The time in minutes that customers stayed in the restaurant was noted for both nights. According to the boxplots, both samples little skew and are approximately symmetric, so both conditions for inference are met. a) For one experimental unit, what is the response variable? Categorical or quantitative? Use the summary statistics and the applet to conduct a significance test to see if use of the scent changes the duration of the average stay. b) How did you define Group 1? Group 2? c) What are the hypotheses? d) What is the P-value? e) What is the conclusion in context of the problem? Be sure to state the conclusion in plain English, not statistics jargon. f) Estimate the difference in mean duration with a 95% confidence interval (using applet). Confidence interval: Do not interpret the interval. Why? Consider that the results of your significance test should be consistent with the 95% confidence interval. Briefly explain why they are consistent, stating the value in Ho and your confidence interval.

Explanation / Answer

a) The time in minutes is the responsible variable and it is quantitative.

b) The customer stayed fewer minutes when the scent is was there as compared to when there no scent was used.

c) The hypothesis is

H0: Mean time (Group 1) = Mean time (Group 2)

H1: Mean time (Group 1) Mean time (Group 2)

d) With t = 0.3714, the p-value = 0.7118

e) Since p-value > 0.05 we conclude that mean time for both the groups is same.

f) Mean Difference = -1.48100

95% confidence interval of this difference: From -9.47005 to 6.50805

The results are consistent with CI as we can see that the interval includes 0.

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