STA10003 FOUNDATIONS OF STATISTICS SWIN BUR NE SWINBURNE UNIVERSITY OF TECHNOLOGY Week 7 Lecture Jascha Zimmermann jzimmermann@swin.edu.au KNOW ING Revision Week 6 If we want to test an hypothesis about a population mean [metric data], we use the One-sample t-test If we want to test an hypothesis about a population proportion [categorical data], we use a Binomial Test These tests are the same conceptually » testing our sample finding to a reference value in the population Once we have produced the output, made our decision, and formed a conclusion we can write up the findings ... KNOW ING 2 1
Facebook times ... A social media researcher thought that young adults spend more time on Facebook per day than indicated by previous research [120 mins per day]. She obtained a random sample of young adults, and asked them how much time per day they spend on Facebook. H0 : Facebook time per day[young adults] ? 120 minutes H1: Facebook time per day [young adults] > 120 minutes Produce the one-sample t-test ... Compare the p-value to the alpha test level [a = 0.050] p <0.050 SIGNIFICANT REJECT H0 p ? 0.050 Not SIGNIFICANT DO NOT REJECT H0 Facebook times ... One-Sample Statistics Std. Deviation 36.391 N Mean Std. Error Mean 1.473 Time spent on Facebook [in mins per day] KNOW ING 3 Previous Research 610 180.27 One-Sample Test Test Value = 120 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Time spent on Facebook [in mins per day] 40.903 609 .000 60.269 57.38 63.16 t(609)=140.90,0p <00.00100000000p <00.050Significantl/IREJECTIH, :H1:[Facebookltimelperlday[youngadults]>1120minutes As expected, young adults do spend more than 120 minutes per day on Facebook. Note: If SPSS shows a value of 0.000, then the report shows p < 0.001 [that is, there is less than 1 in 1000 chances of obtaining this result or one more extreme] KNOW ING 4 2
Report writing for Facebook time ... It was hypothesised that, on average, young adults spend more than 120 minutes per day on Facebook. In a random sample of 610 young adults, the average [mean] time spent on Facebook per day was 180.27 minutes [s = 36.39 minutes]. This is higher than indicated by previous research, [120 minutes per day], and a one-sample t-test shows that the difference in the average [mean] Facebook time is significant, t(609) = 40.90, p < 0.001. The 95% confidence interval indicates that, on average, young adults spend between 57.38 minutes and 63.16 minutes more per day on Facebook than indicated by previous research. As expected, young adults do spend more than 120 minutes per day on Facebook. KNOW ING 5 Summarising the One-sample t-test ... Assumptions underpinning the one-sample t-test Independence of observations: » Each observation [score] must be independent of any other » This assumption is usually satisfied if a random sample is selected Population must be normally distributed: » Critical values / tables for the t-distributions / t- statistics are mathematically based on a normal distribution > In