# Sample Paper on mean height of the male university students in the USA

Descriptive statistics

Executive summary

This project seeks to test the null hypothesis that the mean height of the male university students in the USA is always equal to 70 inches against an alternative hypothesis that this mean is not equal to 70 inches. In order to test this hypothesis, I will collect the height of 110 male university students in our university by simply asking them about their height. After collecting this data, then I will input it in an excel program to determine the mean, standard deviation and standard variance. I will also determine the mode, median and the sample’s range. The p-value will be 5% while the confidence level will be 95%. Once I calculate the mean, standard deviation and standard error, I will test the null hypothesis using the t distribution.

Introduction

It is hypothesized that the mean height of the male university students in the USA is 70 inches. In this test, I will be interested in testing this hypothesis. Therefore, in order to test it, I will randomly collect a sample height of 110 male students from our university by asking them about their heights. After collecting this sample, then I will input the data in excel program and calculate the mean, standard deviation and standard variance. I will also calculate the mode, median and range (Anderson, Sweeney and Williams 143). Then with the help of these data, I will test the null hypothesis using the t test.

Analysis

The p-value for this test is 0.05 (5%) while the confidence level is 95%.

For the confidence interval level, the upper and the lower limits will be µ ± 0.236318723. This means the upper limit will be 69.8 + 0.236318723 = 70.26838. On the other hand, the lower limit will be 69.8 – 0.236318723 = 69.33162. We can use this information to see what should happen to the null hypothesis by evaluating whether the hypothesized mean falls within this range or not, but let us use the t-distribution.

The null hypothesis states that the mean height of university students is equal to 70 inches. Conversely, the alternative hypothesis states that the mean height of university students is not equal to 70 inches.

H0: µ = 70;

H1: µ ≠ 70;

This test is a two-tailed test because the null hypothesis uses an equal sign while the alternative hypothesis negates it. At the same time, even though it has been hypothesized that the mean height is equal to 70 inches, it is also possible that this mean might in some instances be less than 70. This means that the test should be two-tailed.

The t-distribution utilizes the following formula to obtain the t value and I will use it to obtain my calculated t value. Then I will compare this value with the critical t value to determine whether I should retain the null hypothesis or reject it.

t = (µ -β)/S.E, where µ is the calculated sample mean, β s the hypothesized mean and S.E is the standard error (Anderson, Sweeney and Williams 143).

After collecting a sample data of 110 students and analyzing that data using excel program, I have obtained a sample mean of 69.8 inches, a standard deviation of 2.478531675 and a sample variance of 6.143119266. I will utilize these results to test my hypothesis.

 Descriptive statistics Mean 69.8 Standard Error 0.236318723 Median 70 Mode 67 Standard Deviation 2.478531675 Sample Variance 6.143119266 Kurtosis -0.295639266 Skewness -0.064659862 Range 12 Minimum 64 Maximum 76 Sum 7678 Count 110 Confidence Level (95.0%) 0.468376012

(Davis and Pecar 100)

From the above table, it is clear that the sample’s mean is 69.8. To test the null hypothesis I should calculate the critical t value, which in this case is 1.981967. I should also calculate the t value using the formula above for t distribution and obtain -0.846314662. In this case, I will retain the null hypothesis if the calculated t value will be less than the critical t. On the contrary, I should reject it if it will be greater than the critical t value. Since the t value is less than the critical t then I should retain the null hypothesis (Davis and Pecar 100). This means that I should accept the hypothesis that the mean height of the male university students in the USA is 70 inches.

Summary/conclusion

In summary, the mean is 69.8, standard deviation 2.478531675 and variance 6.143119266. Furthermore, the critical t value is 1.981967 while the calculated t value is -0.846314662. This data demonstrates that I should accept the null hypothesis that claims that the mean height of the male university students in the USA is 70 inches because the hypothesized mean falls within the upper and the lower limits. At the same time, I should retain the null hypothesis because the value of the calculated t is less than the value of critical t. By accepting this hypothesis, I should reject the alternative hypothesis that states otherwise and conclude that the mean height of the male university students in the USA is 70 inches.

Works Cited

Anderson, David, Sweeney, Dennis, and Williams Thomas. Statistics for business and economics. Mason: Cengage learning. 2010.

Davis, Glyn, and Pecar Branko. Business Statistics Using Excel. Oxford: Oxford University Press, 2013. Print.

Appendix (data collected and used)

 71 70 71 67 67 70 73 67 67 71 70 70 69 72 68 68 73 67 67 71 72 70 67 68 72 67 71 74 70 70 74 74 71 67 67 73 70 70 70 67 72 72 67 71 75 68 74 67 68 71 68 72 72 69 70 71 69 73 70 69 73 69 71 71 69 72 72 76 72 72 67 71 65 67 68 69 71 65 67 72 72 65 70 64 69 67 73 69 75 70 72 71 64 65 67 69 72 71 69 71 70 71 70 69 67 68 68 71 70 69