Question

A study conducted by Pennsylvania State University researchers investigated whether time perception, an indication of a person’s ability to concentrate, is impaired during nicotine withdrawal. After a 24-hour smoking abstinence, a random sample of thirty smokers was asked to estimate how much time (in seconds) had elapsed during an actual 45-second time period test. Summary statistics are shown in the table below.

Sample Mean = 50.35 seconds | Sample Standard Deviation = 19.84 seconds

a) Find a 90% confidence for the perceived true population mean time lapse by smokers for an actual 45-second time period test. Be sure to attach the units of measure.

b) Prior to this study, the researchers believed that, on average, smoking abstinence leads to elapsed time being overestimated during nicotine withdrawal. Comment on their belief based your statistical results in (8a) above.

Answer 1

(a) 90% CI for true population mean

CI = Mean + /- E

t value using excel formula.

TINV( , df) = TINV (0.10, 29) = 1.699

E = 6.155 sec

CI = 50.35 + /- 6.155

CI = (44.195 sec , 56.505 sec)

(b)

Ho: = 45

Ha: > 45

As the population mean 45 sec is within the CI range, we fail to reject the Null hypothesis.

Hence, we do not have sufficient evidence to believe that on average, smoking abstinence leads to elapsed time being overestimated during nicotine withdrawal.