Question

12. A study conducted by researchers at Pennsylvania State University investigated whether time perception, an indication of a person’s ability to concentrate, is impaired during nicotine withdrawal. The study results were presented in the paper “Smoking abstinence impairs time estimation accuracy in cigarette smokers” (Psychopharmacology Bulletin [2003]: 90-95).

After a 24-hour smoking abstinence, 25 smokers were asked to estimate how much time had elapsed during a 45-second period. Suppose the resulting data on perceived elapsed time (in seconds) were as follows:

The sample mean was 59.3, s = 9.84. Assuming the data is approximately normally distributed, test by hypothesis at the 5% level whether the perceived elapsed time was different from 45 seconds.

Answer 1

Let $\mu$ denotes the mean perceived elapsed time.

To test
Ho 45 0
against
1

Here

sample mean

593

sample standard deviation

S=9.84

and sample size

n25

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

Vn(-45) t =

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

tobs =7.2663

P-value =

P(tn-1 tobs) = P(t24> 7.2663) 2*P(t>7.2663) 2* (1-1)0

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that the perceived elapsed time was significantly different from 45 seconds