## Related questions with answers

A university employment office wants to compare the time taken by graduates with three different majors to find their first full-time 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 2009.

Business | Computer Science | Engineering |
---|---|---|

136 | 156 | 126 |

162 | 113 | 151 |

135 | 124 | 163 |

180 | 128 | 146 |

148 | 144 | 178 |

127 | 147 | 134 |

176 | 120 | |

144 |

At the $5 \%$ significance level, can you conclude that the mean time taken to find their first full-time job for all May 2009 graduates in these fields is the same?

Solutions

VerifiedSince we have three different majors, which represents three different population samples, and their means, we will use one-way ANOVA and the $F$ distribution to test the null hypothesis that these three means are the same.

Null and alternative hypothesis are:

- $H_0:$ $\mu_1 = \mu_2 = \mu_3$,
- $H_1:$ Not all population means are equal,

where $\mu_1$, $\mu_2$ and $\mu_3$ are mean time taken to find first full-time job for bussiness majors, computer science majors and engineering majors respectively.

Take note that all the conditions of a one-way ANOVA procedure are satisfied, i.e.

- the populations have equal variances;
- the populations from which the samples are obtained are normally distributed; and
- the populations from which the samples are obtained are random and independent.

The following problem constitutes three populations containing values representing time (in days). You are given a $5$% significance level to test the hypothesis.

To solve for this, the whole solution process is structured by these steps:

- State the null and alternative hypothesis
- Choose the appropriate distribution for testing
- Determine areas of acceptance/rejection
- Find the Test Statistic
- Make the decision

**Stating the Null $\bold{(H_0)}$ and Alternative $\bold{(H_1)}$ Hypotheses**
Most of the time, stating the null hypothesis is incorporated by concepts of *"equal"* or the state of *"not being"*. Therefore you can start with the null hypothesis stating that the means are **equal** (as it is also stated in the problem) while the alternative hypothesis contains the **opposite** statement.

- $H_0$: There is no significant difference between the mean time (in days) it takes for the graduates to find their first job in the different fields.
- $H_1$: There is a significant difference between the mean time (in days) it takes for the graduates to find their first job in the different fields.

$\text{OR}$

$\begin{aligned} H_0&: \mu_1=\mu_2=\mu_3\\ H_1&: \mu_1\neq\mu_2\neq \mu_3 \end{aligned}$

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