A study conducted by researchers at Pennsylvania State University investigated w
ID: 3151572 • Letter: A
Question
A study conducted by researchers at Pennsylvania State University investigated whether time perception, and indication of a person’s ability to concentrate, is impaired during nicotine withdrawal. The study results were summarized in the paper “Smoking Abstinence Impairs Time Estimation Accuracy in Cigarette Smokers” (Psychopharmacology Bulletin {2003}: 90-95). After a 24-hour smoking abstinence, 20 smokers were asked to estimate how much time had passed during a 45-second period. Suppose the resulting data on perceived elapsed time (in seconds) were as follows
time<-c(69, 65, 72, 73, 59, 55, 39, 52, 67, 57, 56, 50, 70, 47, 56, 45, 70, 64, 67, 53)
Does this information indicate that the perceived elapsed time is more than 45 seconds? Use a 0.05 level of significance. Make sure you show all the steps of the hypothesis test.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 45
Ha: u > 45
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 19
tcrit = + 1.729132812
Getting the test statistic, as
X = sample mean = 59.3
uo = hypothesized mean = 45
n = sample size = 20
s = standard deviation = 9.836024015
Thus, t = (X - uo) * sqrt(n) / s = 6.501767794
Also, the p value is, as this is right tailed,
p = 1.57269E-06
As t > 1.729, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the perceived elapsed time is more than 45 seconds at 0.05 level. [CONCLUSION]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.