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# Exam H

You can download the combined lecture notes for this module at:
<https://asta.math.aau.dk/course/asta/2018-2/cph-bd/lecture/5-exam?file=H/module-H.pdf>

Remember to load the `mosaic` package first:
```{r message=FALSE}
library(mosaic)
```


## Data collection

* Describe your data collection strategy and considerations (including weaknesses) in your project (or a previous/future/others'/...). This probably includes the following:
    + Very briefly what your project is about.
    + The ideal population/target group/market segment (the ones you ideally would like to make inference about).
    + Describing and discussing the sampling scheme, both advantages and disadvantages (e.g. practical as time/money).
    + Discussed the measured quantities and their status (for controlling, are there any potential lurky or confounding variables).
    + Describe the generalisability of your sample. Is it a true, random sample from the population of interest?

If you do not have a project with data collection, you can use this case: <https://plast.dk/wp-content/uploads/2017/07/Plast-og-kemi-survey-af-danskernes-holdning-2017.pdf>.


## Berkeley admission

### Six largest departments

The following table shows the total number of admitted and rejected applicants to the six largest departments in Berkeley in 1973.

|       | Admitted| Rejected|
|:------|--------:|--------:|
|Male   |     1198|     1493|
|Female |      557|     1278|

Use a $\chi^2$-test to check whether the admission statistics for
Berkeley show any sign of gender discrimination. To enter the table
in R you can do:

```{r}
admit <- matrix(c(1198, 557, 1493, 1278), 2, 2)
rownames(admit) <- c("Male", "Female")
colnames(admit) <- c("Admitted", "Rejected")
admit <- as.table(admit)
```

Your analysis should as a minimum contain:

- Statement of hypotheses
- Calculation and explanation of expected frequencies
- Calculation and explanation of test statistic
- Calculation and interpretation of p-value
- If relevant, interpretation of the standardized residuals

### For each department

In the following, results are given for when each department is analyzed individually. 
Explain what is happening (also in relation to the previous problem 
with the overall numbers for all six departments combined).

#### Department A

|         | Male| Female|
|:--------|----:|------:|
|Admitted |  512|     89|
|Rejected |  313|     19|

p-value = $5.2 \times 10^{-5}$.

Standardized residuals:

|         |      Male|    Female|
|:--------|---------:|---------:|
|Admitted | -4.153073|  4.153073|
|Rejected |  4.153073| -4.153073|

#### Department B

|         | Male| Female|
|:--------|----:|------:|
|Admitted |  353|     17|
|Rejected |  207|      8|

p-value = 0.77.

#### Department C

|         | Male| Female|
|:--------|----:|------:|
|Admitted |  120|    202|
|Rejected |  205|    391|

p-value =  0.43.

#### Department D

|         | Male| Female|
|:--------|----:|------:|
|Admitted |  138|    131|
|Rejected |  279|    244|

p-value = 0.64.

#### Department E

|         | Male| Female|
|:--------|----:|------:|
|Admitted |   53|     94|
|Rejected |  138|    299|

p-value =  0.37.

#### Department F

|         | Male| Female|
|:--------|----:|------:|
|Admitted |   22|     24|
|Rejected |  351|    317|

p-value = 0.64.