The amount of protein (in grams) for a variety of fast-food sandwiches is reported here

```
23 30 20 27 44 26 35 20 20 29
25 15 18 27 19 22 12 26 34 15
27 35 26 43 35 14 24 12 23 31
40 35 38 57 22 42 24 21 27 33
```

a. Construct a dot plot.

b. Find the proportion fast-food sandwiches with at most 37 grams.

c. Find the proportion of fast-food sandwiches with at least 40 grams.

#### Solution

```
protein<-c(23, 30, 20, 27, 44, 26, 35, 20, 20,
29, 25, 15, 18, 27, 19, 22, 12, 26, 34, 15, 27,
35, 26, 43, 35, 14, 24, 12, 23, 31, 40, 35, 38,
57, 22, 42, 24, 21, 27, 33)
```

(a) dotchart of amount of protein

`dotchart(protein,xlab="amount of protein")`

b. The Proportion fast-food sandwiches with at most 37 grams

```
most37<-protein[protein<=37]
most37
```

```
[1] 23 30 20 27 26 35 20 20 29 25 15 18 27 19 22 12 26 34 15 27 35 26 35 14 24
[26] 12 23 31 35 22 24 21 27 33
```

```
prop37<-length(most37)/length(protein)
prop37
```

`[1] 0.85`

Proportion fast-food sandwiches with at most 37 grams is 0.85.

c. The proportion of fast-food sandwiches with at least 40 grams.

```
least40<-protein[protein>=40]
least40
```

`[1] 44 43 40 57 42`

```
prop40<-length(least40)/length(protein)
prop40
```

`[1] 0.125`

Proportion fast-food sandwiches with at least 40 grams is 0.125.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators