Find a statistic that is expected to be normally distributed (e.g. height of adult men). · Sample 30 people regarding their value related to this statistic (e.g. ask them “How tall are you?”) and record your results. Sampling 30 people is not optional. You must have at least 30 values of the statistic you choose. · Use StatCrunch to create a histogram of your results. · Post the question you asked and the histogram you created. Are your results normally distributed? Why or why not?
In this assignment, we are required to find a statistic that is expected to be normally distributed and sample 30 people regarding their values related to this statistic. We will then use StatCrunch to create a histogram of the results and determine if they are normally distributed or not.
To fulfill this requirement, I have chosen the statistic of body weight of adult women. This statistic is often assumed to follow a normal distribution. I will sample 30 women and ask them “How much do you weigh?” to collect the data required for this assignment.
Now that the data has been collected, I will proceed to analyze it and create a histogram using StatCrunch. A histogram is a graphical representation that displays the distribution of a continuous variable. It is an effective tool to visualize the shape of the data and identify its distribution.
After creating the histogram, I will assess if the results are normally distributed or not. The normal distribution, also known as the Gaussian distribution or bell-shaped curve, is characterized by its symmetric shape and specific mean and standard deviation values. Many natural phenomena and statistical processes are expected to follow this distribution.
To determine if the results are normally distributed, we need to examine the shape of the histogram. If the histogram is approximately symmetric and follows the shape of a bell curve, it suggests that the data may be normally distributed. Conversely, if the histogram exhibits a skewed or irregular shape, it indicates that the data does not follow a normal distribution.
Once the histogram is created, I will carefully examine its shape and assess if it resembles a normal distribution. Based on the visual appearance of the histogram, I will make a preliminary determination of whether the results are normally distributed or not.
In my analysis, I will also consider the sample size of 30. According to the Central Limit Theorem, as the sample size increases, the distribution of the mean of a random sample will become more approximately normally distributed, regardless of the shape of the population distribution. With a sample size of 30, we can expect the distribution of the mean to be close to normal even if the underlying population distribution is not normally distributed.
Therefore, even if the histogram does not perfectly resemble a bell-shaped curve, it is still possible for the results to be considered approximately normally distributed due to the sample size. This is assuming that the data follows other assumptions of the Central Limit Theorem, such as independence and sufficiently large sample.
In conclusion, we have selected the statistic of body weight of adult women, sampled 30 women, and collected their responses to the question “How much do you weigh?” Using StatCrunch, we have created a histogram of the results. To determine if the results are normally distributed or not, we have carefully examined the shape of the histogram and considered the sample size. From this analysis, we can evaluate whether the results follow a normal distribution or not.