Question 1
A school psychologist reports that the mean number of hours the students at this school sleep each night is 8 hours. The students believe the mean is not 8 hours. To find an estimate of the true mean, they select a random sample of 15 students from their school and ask how many hours each slept last night.
A stemplot and boxplot of the numbers of hours are shown here.
Plots are not shown. Copy and paste might not be working.
Also, what is your question?
To estimate the true mean number of hours the students at the school sleep each night, the students selected a random sample of 15 students and asked each student how many hours they slept last night. The stemplot and boxplot provided can help us analyze the data.
The stemplot is a graphical representation of the data that shows the individual values or scores. It helps us identify the shape and distribution of the data. The stemplot for this data is not provided in the question, so we won't be able to use it to analyze the data.
The boxplot, on the other hand, provides a visual summary of the data that includes the minimum value, lower quartile, median, upper quartile, and maximum value. It also helps us identify any outliers, which are values that significantly differ from the rest of the data.
To analyze the boxplot, we need to understand its components:
- The minimum value represents the smallest observed value in the dataset.
- The lower quartile (Q1) represents the value below which 25% of the data falls.
- The median represents the middle value in the dataset, dividing it into two equal halves.
- The upper quartile (Q3) represents the value below which 75% of the data falls.
- The maximum value represents the largest observed value in the dataset.
- The central box represents the interquartile range (IQR), which is the range between the lower and upper quartiles.
- Any points outside of the whiskers (lines extending from the box) are considered outliers.
By examining the boxplot, we can compare the median (or the middle line inside the box) to the reported mean of 8 hours. If the median is significantly different from 8 hours, it suggests that the true mean may also be different. We can also look for any outliers that may indicate extreme values that could affect the mean.
Without the stemplot, we won't have a complete picture of the data, but we can still make some assumptions based on the boxplot. If the median is close to 8 hours and there are no outliers, it suggests that the sample data supports the reported mean of 8 hours. However, if the median varies significantly from 8 hours or there are outliers, it may indicate a discrepancy between the reported mean and the true mean.
To get a more accurate estimate of the true mean, it would be helpful to have access to the stemplot and gather more data by sampling a larger number of students. This would increase the sample size and provide a more representative sample of the student population.