Question

A large company wants to find out what team-building activity its employees prefer. Which of the following samples can give the most valid generalization?(1 point)
Responses

400 randomly chosen employees from the list of all employees
400 randomly chosen employees from the list of all employees

all 624 female employees in the company
all 624 female employees in the company

all employees who have worked in the company for 5 years or more
all employees who have worked in the company for 5 years or more

a group with one member from each department
A hotel maintenance crew wants to estimate how many of the 12,000 lamps in their 30-story hotel need a new light bulb. Which of the following is a random sample of lamps to be inspected?(1 point)
Responses

all lamps in booked rooms
all lamps in booked rooms

all lamps from the rooms with king-sized beds
all lamps from the rooms with king-sized beds

400 lamps on the first 10 floors
400 lamps on the first 10 floors

100 lamps on each floor chosen randomly
A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number. (1 point)
patrons
Use the table to answer the question.

This table displays the shopping time taken by Group A and Group B for comparison.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is
minutes.
The mean time Group B spent shopping is
minutes.
The mean times Group A and Group B spent shopping differ by
minutes.
Which data set has the highest median?(1 point)
Responses

{1, 6, 15, 7, 15, 18, 14}
left brace 1 comma 6 comma 15 comma 7 comma 15 comma 18 comma 14 right brace

{1, 10, 8, 29, 14, 17, 3}
left brace 1 comma 10 comma 8 comma 29 comma 14 comma 17 comma 3 right brace

{11, 15, 16, 8, 12, 14}
left brace 11 comma 15 comma 16 comma 8 comma 12 comma 14 right brace

{8, 20, 13, 14, 12, 9}

Answer 1

Let's address each question step by step:

### 1. Sample Generalization
To determine which sample provides the most valid generalization for the team-building activity preference:

- **400 randomly chosen employees from the list of all employees**
- All other options are biased or not representative of the entire employee population.

**Most valid sample: 400 randomly chosen employees from the list of all employees.**

### 2. Random Sample of Lamps
To estimate how many of the 12,000 lamps in a 30-story hotel need a new light bulb, the best sampling method for random selection would be:

- **100 lamps on each floor chosen randomly**

This ensures that every floor is represented in the sample.

### 3. Estimating the Number of Patrons Borrowing Novels
If 3 out of 80 patrons borrow novels, then the proportion of patrons borrowing novels can be calculated as:

\[
\text{Proportion} = \frac{3}{80}
\]

To find out how many of the 345 patrons borrow novels, we multiply:

\[
\text{Number of patrons} = \frac{3}{80} \times 345 = 12.9375
\]
Rounding to the nearest whole number gives us approximately **13 patrons.**

### 4. Mean Times and Differences
To find the mean times each group spent shopping:

- For **Group A**:
\((18 + 20 + 46 + 34 + 58 + 31 + 41) / 7 = 37.7142857\) (Rounded to 37.7 minutes)

- For **Group B**:
\((15 + 21 + 32 + 42 + 29 + 57 + 39) / 7 = 32.4285714\) (Rounded to 32.4 minutes)

**Mean time Group A is 37.7 minutes.**
**Mean time Group B is 32.4 minutes.**
**Difference in mean times: \(37.7 - 32.4 = 5.3\) minutes.**

### 5. Highest Median
To find the highest median:

1. **Sort and Find Each Median**:
- {1, 6, 15, 7, 15, 18, 14} → sorted: {1, 6, 7, 14, 15, 15, 18}; Median is 14.
- {1, 10, 8, 29, 14, 17, 3} → sorted: {1, 3, 8, 10, 14, 17, 29}; Median is 10.
- {11, 15, 16, 8, 12, 14} → sorted: {8, 11, 12, 14, 15, 16}; Median is 13.
- {8, 20, 13, 14, 12, 9} → sorted: {8, 9, 12, 13, 14, 20}; Median is 12.5.

**Highest median is 14 from the first data set.**

In summary:
1. Most valid generalization sample: **400 randomly chosen employees**
2. Random sample of lamps: **100 lamps on each floor chosen randomly**
3. Approximate number of patrons borrowing novels: **13 patrons**
4. Mean shopping times: Group A = **37.7 minutes**, Group B = **32.4 minutes**, difference = **5.3 minutes**
5. Data set with the highest median: **{1, 6, 15, 7, 15, 18, 14}** (Median = 14)