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In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a nonbrowser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected. Use \(\alpha=.05\) to test for differences among comfort levels for the three types of browsers. $$\begin{array}{ccc} & \text { Light } & \text { Heavy } \\ \text { Nonbrowser } & \text { Browser } & \text { Browser } \\ 4 & 5 & 5 \\ 5 & 6 & 7 \\ 6 & 5 & 5 \\ 3 & 4 & 7 \\ 3 & 7 & 4 \\ 4 & 4 & 6 \\ 5 & 6 & 5 \\ 4 & 5 & 7 \end{array}$$

Short Answer

Expert verified
Perform an ANOVA test. If F-calculated > F-critical, there are significant differences among groups.

Step by step solution

01

Formulate Hypotheses

The null hypothesis ( H_0 ) states that there are no differences among the comfort levels of nonbrowser, light browser, and heavy browser shoppers. The alternative hypothesis ( H_1 ) states that at least one group of browser type has a different comfort level than the others.
02

Select Significance Level

The significance level is given as a=0.05 .
03

Arrange Data for ANOVA

The data is provided for three groups: Nonbrowser, Light Browser, and Heavy Browser. Arrange them into three separate datasets: \(Nonbrowser: [4, 5, 6, 3, 3, 4, 5, 4]\),\(Light\ \Browser: [5, 6, 5, 4, 7, 4, 6, 5]\),\(Heavy\ \Browser: [5, 7, 5, 7, 4, 6, 5, 7]\).
04

Calculate Means for Each Group

Find the mean of each group: \(\bar{x}_{Nonbrowser} = \frac{4+5+6+3+3+4+5+4}{8} = 4.25\),\(\bar{x}_{Light\ Browser} = \frac{5+6+5+4+7+4+6+5}{8} = 5.25\),\(\bar{x}_{Heavy\ Browser} = \frac{5+7+5+7+4+6+5+7}{8} = 5.75\).
05

Perform ANOVA Test

Conduct an ANOVA test to determine if the differences in means are statistically significant. Calculate the variance within each group and between groups. Compare the F-value from the ANOVA calculation to the critical F-value from F-distribution tables for \(\alpha=0.05\). If F-calculated > F-critical, reject the null hypothesis.
06

Conclude the Results

After performing the ANOVA, check if the calculated F-value is greater than the critical F-value for two degrees of freedom for numerator (k-1) and, for the denominator (N-k), where k is the number of groups and N is the total number of observations. If it is, it implies significant differences among the groups. Otherwise, no significant difference is found.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Browsing Behavior
In studies that involve shopping and consumer behavior, understanding browsing behavior is essential. Browsing behavior refers to how shoppers interact with products or services in a retail environment.

There are generally three categories of browser types:
  • Nonbrowser: These are shoppers who do not spend time looking around and typically know what they want to purchase before entering the store.
  • Light Browser: These shoppers spend some time looking around but are not extensively involved in browsing. They might randomly look at items or return to familiar products.
  • Heavy Browser: These individuals spend a significant amount of time in the store actively engaging with various products, examining details, and comparing options.


This kind of categorization helps researchers and businesses determine consumer comfort levels and preferences, allowing for better store layouts, targeted marketing, and improved customer service. Understanding these behaviors can significantly impact business strategies and customer satisfaction levels.
Hypothesis Testing
Hypothesis testing is a fundamental component of statistical analysis, providing a mechanism to make decisions about data. In this exercise, the focus is to test if there are differences among comfort levels for different browser types.

Hypothesis testing typically involves two main hypotheses:
  • Null Hypothesis (\(H_0\)): This hypothesis assumes that there are no differences among the groups being compared—in this case, the comfort levels for nonbrowser, light browser, and heavy browser shoppers are statistically the same.
  • Alternative Hypothesis (\(H_1\)): This suggests that there is at least one significant difference in comfort levels among the different browsing groups.


By conducting an ANOVA test, you evaluate these hypotheses using an appropriate significance level, given as \(\alpha = 0.05\) in this exercise. If the computed p-value is less than the significance level, \(H_0\) is rejected, suggesting meaningful differences among the groups. This statistical tool helps determine if any observed variations are likely the result of random chance or reflect actual differences in consumer experience.
Comfort Level Assessment
Comfort level assessment measures how at ease or satisfied shoppers feel within a store environment. This is typically done through surveys or observational methods where higher scores indicate greater levels of comfort.

The exercise collected data to determine how comfortable different types of browsers feel, scoring comfort level on a numerical scale. Assessing comfort levels can provide insights into customer preferences and store effectiveness in creating a welcoming atmosphere.

Several factors contributing to comfort level include:
  • Store layout and organization: A well-organized store allows for easy navigation, enhancing customer experience.
  • Customer service quality: Polite, knowledgeable, and helpful staff can positively affect a shopper's comfort.
  • Ambience and aesthetics: Appropriate lighting, sound, and visual displays can create a pleasant environment.
  • Product availability and variety: Having desired products readily available meets consumer needs and elevates comfort.


The assessment helps retailers improve areas that might impact shopper comfort negatively, thereby potentially increasing consumer satisfaction and encouraging return visits.

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Most popular questions from this chapter

Consider the following hypothesis test. $$\begin{array}{l} H_{0}: \mu_{1}-\mu_{2}=0 \\ H_{\mathrm{a}}: \mu_{1}-\mu_{2} \neq 0 \end{array}$$ The following results are for two independent samples taken from the two populations. $$\begin{array}{ll} \text { Sample 1 } & \text { Sample 2 } \\ n_{1}=80 & n_{2}=70 \\ \bar{x}_{1}=104 & \bar{x}_{2}=106 \\ \sigma_{1}=8.4 & \sigma_{2}=7.6 \end{array}$$ a. What is the value of the test statistic? b. What is the \(p\) -value? c. With \(\alpha=.05,\) what is your hypothesis testing conclusion?

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