Statistics Statistics



The determination of whether the significant departure of temperaturefrom its average requires an understanding of various conditions andfactors that could have resulted in the change. In the casepresented, there is a change from the average 60 to a record 70.Descriptive statistics could be used to explain why there is adifference in the temperatures. Additional information that could beapplicable in the case regards the concept of factors that may haveled to a shift in the overall temperatures (Cao, Ewing, &ampThompson, 2012). For example, it could be mandatory to have anunderstanding of the cloud cover of the region at the time when thetemperature readings were taken (Choi, Kim, Jung, Kim, &amp Park,2014). Also, information such as aspect about the direction of thesun may be vital in helping describe why there is a significantchange in the temperature (Intergovernmental Panel on Climate Change,2014). Descriptive statistics could be essential in helping explainthe significant changes in temperature.

However, in understanding the concept better, it could be crucial toelaborate the phenomena using descriptive statistics. The independentvariable would be the temperatures. The dependent variable includesthe cloud cover and aspect (Cools, &amp Creemers, 2013). A change incloud cover has an impact in influencing the temperature on the givenday. Similarly, aspect affects the temperature readings taken on agiven day (Summerfield, 2014). The two variables are employed inexplaining the variations in temperature from the average of 60 to arecord high of 70. The scale of measurements applied is nominal andordinal. Temperature readings are recorded numerically, while thecloud cover and aspect measurements are observed. However, it isessential to assume factors such as the location, humidity and thedays of the year (Rosenzweig, &amp Udry, 2014). An assumption of thefact that there is no change in latitude is crucial sincetemperatures are taken for the particular location.


Cao, Q., Ewing, B. T., &amp Thompson, M. A. (2012). Forecasting windspeed with recurrent neural networks. European Journal ofOperational Research, 221(1), 148-154.

Choi, S. J., Kim, E. B., Jung, W. S., Kim, B. J., &amp Park, J. K.(2014). Analysis of Utilization and Perception of Special WeatherReports for Climate Change Adaptation: Focus on Dryness Advisory andWarning. Journal of Environmental Science International,23(6), 1121-1130.

Cools, M., &amp Creemers, L. (2013). The dual role of weatherforecasts on changes in activity-travel behavior. Journal ofTransport Geography, 28, 167-175.

Intergovernmental Panel on Climate Change. (2014). Climate Change2014–Impacts, Adaptation and Vulnerability: Regional Aspects.Cambridge University Press.

Rosenzweig, M. R., &amp Udry, C. (2014). Rainfall forecasts,weather, and wages over the agricultural production cycle. TheAmerican Economic Review, 104(5), 278-283.

Summerfield, M. A. (2014). Global geomorphology. Routledge.




NullHypothesis (H0)

Thenull hypothesis refers to the default statement showing there is norelationship between two phenomenons being investigated (Minitab,2016). It is usually the common view of an issue. For thisparticular study, the null hypothesis is:

H0:There is no correlation between the performance of the 6th graders ona math lesson and background noise level.

Alternativehypothesis (H1)

Onthe other hand, alternative hypothesis (H1)indicates that sample observations are not influenced by anyparticular non-random cause. Simply put, it is what a researcherintends to prove to be true. For this case

H1: There is a correlation between the performance of the 6th graders ona math lesson and background noise level.

Whatare the assumptions that must be met about her data before she cancorrectly use an independent t-test to test the hypotheses? Why?

Thereare six notable assumptions that Mary must make to ensure successfuluse of independent t-test.

Assumption#1: The dependent variable should be measurable on a scale that iscontinuous. This is crucial as it ensures that data is collected atratio or interval level.

Assumption#2: Independent variable should consist of two independent groupsthat are categorical for example male or female, employed orunemployed among others.

Assumption#3: There should be independent observations. This is important inensuring there exist no relationship between the observations in anyof the groups.

Assumption#4: There ought not to exist significant outliers to ensure all datacollected follows a particular pattern.

Assumption#5: The dependent variable must e normally distributed for all thegroups of independent variables.

Assumption#6:There should be homogeneity of variances (LaerdStatistics, 2013).

Howwould she see if her data meet these assumptions?

Whenusing SPSS, Mary can use Levene’stest to test for assumptions number 4, 5 and 6. The rest can bechecked by Mary prior to collection of data.

Howmuch room does she have to violate any of these assumptions and stillget accurate results from the t-test?

Itis worth noting that, there is no room for violating any of theseassumptions. This is based on the premise that, for independentt-test, all the above assumptions must have been met in totality(LaerdStatistics, 2013).


LaerdStatistics (2013). IndependentT-Test using SPSS Statistics.Retrieved from

Minitab (2016). Aboutthe null and alternative hypotheses.Retrievedfrom

Understandingthe Independent Samples T-Test.Available at