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Chapter 12: Problem 7

Briefly explain when a one-way ANOVA procedure is used to make a test of hypothesis.

Short Answer

Expert verified
A one-way ANOVA procedure is used to make a test of hypothesis when there are more than two independent groups that we're interested in comparing and we are considering one categorical and one continuous variable. It tests if there are any significant differences between the means of these groups.

Step by step solution

01

Understanding of One-Way ANOVA

One-way ANOVA is a statistical method used to test if there are any significant differences between the means of three or more independent (unrelated) groups. It does this by looking at the variance in the data and determining whether the means are truly different or if the differences can be explained just by chance.
02

Defining the Hypothesis Test

In a hypothesis test, we use sample data to make decisions about population parameters. For instance, in one-way ANOVA, we make a hypothesis about the equality of three or more population means.
03

Application of One-Way ANOVA

A one-way ANOVA is used when we want to compare more than two groups and we have one categorical variable (the grouping variable) and one continuous variable. An example might be comparing the average height of players in different sports. The sports are the groups (categorical variable) and the heights are the continuous variable.

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Most popular questions from this chapter

Describe the main characteristics of an \(F\) distribution.

A billiards parlor in a small town is open just 4 days per week-Thursday through Sunday. Revenues vary considerably from day to day and week to week, so the owner is not sure whether some days of the week are more profitable than others. He takes random samples of 5 Thursdays, 5 Fridays, 5 Saturdays, and 5 Sundays from last year's records and lists the revenues for these 20 days. His bookkeeper finds the average revenue for each of the four samples, and then calculates \(\sum x^{2}\). The results are shown in the following table. The value of the \(\sum x^{2}\) came out to be \(2,890,000\). $$ \begin{array}{lcc} \hline \text { Day } & \text { Mean Revenue (\$) } & \text { Sample Size } \\ \hline \text { Thursday } & 295 & 5 \\ \text { Friday } & 380 & 5 \\ \text { Saturday } & 405 & 5 \\ \text { Sunday } & 345 & 5 \\ \hline \end{array} $$ Assume that the revenues for each day of the week are normally distributed and that the standard deviations are equal for all four populations. At a \(1 \%\) level of significance, can you reject the null hypothesis that the mean revenue is the same for each of the four days of the week?

A resort area has three seafood restaurants, which employ students during the summer season. The local chamber of commerce took a random sample of five servers from each restaurant and recorded the tips they received on a recent Friday night. The results (in dollars) of the survey are shown in the table below. Assume that the Friday night for which the data were collected is typical of all Friday nights of the summer season. $$ \begin{array}{ccc} \hline \text { Barzini's } & \text { Hwang's } & \text { Jack's } \\ \hline 97 & 67 & 93 \\ 114 & 85 & 102 \\ 105 & 92 & 98 \\ 85 & 78 & 80 \\ 120 & 90 & 91 \\ \hline \end{array} $$ a. Would a student seeking a server's job at one of these three restaurants reject the null hypothesis that the mean tips on a Friday night are the same for all three restaurants? Use a \(5 \%\) level of significance. b. What will your decision be in part a if the probability of making a Type I error is zero? Explain.

A university employment office wants to compare the time taken by graduates with three different majors to find their first fulltime job after graduation. The following table lists the time (in days) taken to find their first full- time job after graduation for a random sample of eight business majors, seven computer science majors, and six engineering majors who graduated in May 2014 . $$ \begin{array}{ccc} \hline \text { Business } & \text { Computer Science } & \text { Engineering } \\\ \hline 208 & 156 & 126 \\ 162 & 113 & 275 \\ 240 & 281 & 363 \\ 180 & 128 & 146 \\ 148 & 305 & 298 \\ 312 & 147 & 392 \\ 176 & 232 & \\ 292 & & \\ \hline \end{array} $$ At a \(5 \%\) significance level, can you reject the null hypothesis that the mean time taken to find their first full-time job for all May 2014 graduates in these fields is the same?

Find the critical value of \(F\) for the following. a. \(d f=(2,6)\) and area in the right tail \(=.025\) b. \(d f=(6,6)\) and area in the right tail \(=.025\) c. \(d f=(15,6)\) and area in the right tail \(=.025\)
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