Some biologists would like to determine whether nicotine withdrawal affects a pe

Question

Some biologists would like to determine whether nicotine withdrawal affects a person’s ability to concentrate by examining one’s time perception. They conducted an experiment with 20 smokers. After a 24-hour smoking abstinence, they were asked to estimate how much time had passed during a 45 second period. The study found that the average perceived elapsed time is 59.30 seconds with a standard deviation of 9.84 seconds. The collected data shows a strong evidence that the data is normally distributed. You would like to carry out a hypothesis test at significance level of 0.05 to decide whether the true average perceived elapsed time is greater than the actual 45 seconds. Use this information and answer Question 16-28.

Question 16

Question 17

Which of the following is the null hypothesis?

Question 18:

Which of the following is the alternative hypothesis test?

Question 19:

Is this a one-sided or two-sided hypothesis test?

Question 20:

In order to determine whether to use a Z-test or a t-test, what are the helpful criteria in this scenario?

strongly believe underlying distribution is normal

strongly believe underlying distribution is not normal

Would you use a Z-test or a t-test?

Z-test

Question 22:

What is your critical value? (enter the negative critical value if it is a two-sided hypothesis test)

Question 23:

What is the value of test statistic?

Question 24:

Based on your test statistic and the critical value, what is the conclusion of this hypothesis test?

Since the test statistic falls in the reject region, we should accept H1.

Since the test statistic falls in the reject region, we should reject H0.

Since the test statistic falls in the accept region, we should accept H0.

Since the test statistic falls in the do not reject region, we should not reject H0.

Question 25:

What is the P-value?

Question 26:

Based on the P-value, what is the conclusion of this hypothesis test?

Fail to reject H0 at significance level 0.05. There is not strong enough evidence to claim that the true average is greater than 45 seconds.

Accept H0 at significance level 0.05, and conclude that the true average is indeed 45 seconds.

Not enough information to conclude. We would need to collect more information.

Reject H0 at significance level 0.05. The data shows a strong enough evidence to claim that the true average is greater than 45 seconds.

Question 27:

Assuming that reject region is above 48.5 seconds. What is the probability that you would commit a type I error?

Question 28

Assume that the true average perceived elapsed time is 46 seconds. What is the probability that you would commit a type II error with a significance level of 0.05?

= 45 seconds

Explanation / Answer

16)
Parameter of interest
mu = true average perceived elapsed time for all smokers exposed to experiment

17)
H0: mu = 45

18)
H1: mu > 45

19)
It is a one-sided upper tail hypothesis test

20)
sigma is unknown

21)
t-test

22)
For significance level of 0.05, critical value = 1.7291

23)
test statistics, t = (59.3 - 45)/(9.84/sqrt(20)) = 6.499

24)
Since the test statistic falls in the reject region, we should reject H0.

25)
p-value = 0.0000016

26)
Reject H0 at significance level 0.05. The data shows a strong enough evidence to claim that the true average is greater than 45 seconds.

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