## Exam 1

1. #### Question

The waiting time (in minutes) at the cashier of two supermarket chains with different cashier systems is compared. The following statistical test was performed:
```	Two Sample t-test
data:  Waiting by Supermarket
t = 3.8575, df = 132, p-value = 0.9999
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 3.552905
sample estimates:
mean in group Sparag mean in group Consumo
5.859404              3.373846
```
Which of the following statements are correct? (Significance level $5%$)

1. The absolute value of the test statistic is larger than 1.96.
2. A one-sided alternative was tested.
3. The $p$ value is larger than $0.05$.
4. The test shows that the waiting time is longer at Sparag than at Consumo.
5. The test shows that the waiting time is shorter at Sparag than at Consumo.

#### Solution

1. True. The absolute value of the test statistic is equal to 3.857.
2. True. The test aims at showing that the difference of means is smaller than $0$.
3. True. The $p$ value is equal to $1$.
4. False. The test aims at showing that the alternative that the waiting time is shorter at Sparag than at Consumo. The test result is not significant ( $p\ge 0.05$).
5. False. The test result ist not significant ( $p\ge 0.05$).