statistic task

DATA FROM LAST TIME

How Far Does it Jump

In this analysis, we are addressing the question of how far does it jump? What we are talking about with what can jump are the origami frogs that we made in our Stats 3000 recitation class. We were given instruction to make these frogs so they were all made the same. The following are the strict instructions: firstly, were only allowed to do one jump and then we were to measure the distance from lining up the front to the zero-centimeter line then after the jump measure the part of the frog that is the farthest away from the zero-centimeter line.

The method used to summarize the data that was collected using a histogram, a boxplot, and numerical data. The first method that I looked at was the histogram of the data. The histogram is given below.

1. A histogram showing frequency of frog jumps and distance covered

0 1 2 3 4 5 6

Frequency

0 5 10 15 20

Data

Interpretation

From the histogram results we see that majority of the frogs only jumped 10 centimeters and less and only about 4 frogs which jumped farther than 10 centimeters. The bars represent the number of frogs, the x-axis represent the number of jumps while the y-axis represents the distance covered.

1. Box plot

The second method that I used was a boxplot of all the data that was recorded. The boxplot is given below.

5 10 15 20

Interpretation

From this boxplot, we can see that the mean lies between 5 and 10 centimeters. We can also see that there are 3 measurements that are considered as outliers to the rest of the data, this means that there were 3 frogs that jumped further than the rest of the frogs. Therefore, we have to consider if we are going to consider these outliers in answering the question of how far can it jump. Basically, the outliers in the data lead to spurious results and hence should be eliminated from further computations.

1. Hypothesis testing

I also used a hypothesis testing method to see if there is sufficient evidence to say that the mean of the jumps was equal to 15.24 centimeters or more than that. First step is to define my Null hypothesis and my alternative.

H0: mean jumps of the frogs is equal to 15.24cm

H1: mean jumps is greater than 15.24cm

Level of significance is 0.05 which is the critical p-value. The decision criterion is that if calculated p is greater than critical p we fail to reject the null hypothesis and vice versa.

One Sample Test

Data: data

T= -5.7944, df= 23, p-value= 1

Alternative hypothesis: true m:

6.481901 Inf

Sample estimates:

Mean of x

8.483333

From the test results to calculate computed p-value, we can see that they p-value is equal to 1 which 1 more than 0.05, this means that we fail to reject our null hypothesis, so we found evidence in favor if the null hypothesis, we conclude they we found sufficient evidence that the mean distance that the frogs jumped was less than 15.24 centimeters.

1. Descriptive statistics

The next method that I used to summarize the data was the descriptive statistics of numerical data where considered the measures of central tendency and the spread. I looked at the minimum, the median, and the mean (which we know is less than 15.24 centimeters) the standard deviation, and the maximum, before I did any of these I looked at a 95% confidence interval for the mean jumping distance of the frogs. The interval came out to be (6.067588, 10899079). With this interval, we are 95% confident that this interval contains the true mean of the distance the frogs can jump, now to get the true mean of the true mean of the data and to look at other numerical data.

The minimum of this data was 1.5 centimeters, the median was 7.25 centimeters, the mean was 8.48333 centimeters, the standard deviation was 4.420951 centimeters, and the maximum was 23 centimeters, this numerical data, in my opinion, is the best way to tell how far the frogs jumped and is a great way to answer the question in this analysis.

From all the methods used, we found some great information based on our data from our class frogs. We found that our mean was less than 15.24 centimeters from our hypothesis test and then we found some other numerical data that helped me to answer the question “how far can it jump”.

So, how far can it jump? From the numerical data, we see that the frog that jumped the furthest jumped 23 centimeters, but this Is not how far is can jump because as we can see from the boxplot this is an outlier and not many frogs could jump that far. So, I decide to say that the frogs can jump as far as the true mean or lower because that was where most of the frogs in our class landed. So finally, I can conclude that the frogs can jump to 8.48 centimeters or less.

Assumptions of the study

For this analysis, we had to assume a couple of things about the data that was gathered. First, we had to assume that everyone used the same force to push down on the back of the frog to make the frog jump forward. Second, we had to assume that everyone measured the way that we were showed before going to collect the data. An additional question that I have about gathering is that does it affect the way the frog jumps if you do a wrong fold or build the frog wrong then use the same paper and correctly fold/build the frog.

Sample estimated: Mean of X 8.48333