A researcher believes that a common over-the-counter medication for arthritis, A

Question

A researcher believes that a common over-the-counter medication for arthritis, Advil, will have a negative effect on driving ability when administered in high doses. You ask a group of seven adults who have arthritis and use Advil to participate in a driver simulation task while under the influence of a high amount of Advil. You record the following braking times (in seconds) required to stop upon seeing a car stopped ini the same lane in front of them. You expect the Advil drivers to have significantly retarted or slower (hence longer braking times, or increased braking times) braking times than the normative group. The mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is = 0.7 seconds. Remember, higher braking time scores mean that the individual is "slow", and the researcher expects Advil will slow braking times.

Braking times (in seconds)

1.2

1.0

1.1

1.4

0.9

1.0

1.6

A researcher believes that a common over-the-counter medication for arthritis, Advil, will have a negative effect on driving ability when administered in high doses. You ask a group of seven adults who have arthritis and use Advil to participate in a driver simulation task while under the influence of a high amount of Advil. You record the following braking times (in seconds) required to stop upon seeing a car stopped ini the same lane in front of them. You expect the Advil drivers to have significantly retarted or slower (hence longer braking times, or increased braking times) braking times than the normative group. The mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is = 0.7 seconds. Remember, higher braking time scores mean that the individual is "slow", and the researcher expects Advil will slow braking times.

Braking times (in seconds)

1.2

1.0

1.1

1.4

0.9

1.0

1.6

Explanation / Answer

Solution:

Here, we have to use one sample t test for the population mean.

Null hypothesis: H0: The mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is 0.7 seconds.

Alternative hypothesis: Ha: The mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is greater than 0.7 seconds.

H0: = 0.7 versus Ha: > 0.7

This is a one tailed test. This is an upper tailed or right tailed test.

We are given

Level of significance = = 0.01

The test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

From given data, we have

Sample mean = Xbar = 1.171428571

Sample standard deviation = S = 0.249761791

Sample size = n = 7

Degrees of freedom = n – 1 = 7 – 1 = 6

Upper critical value = 3.1427 (by using t-table or excel)

Test statistic = t = (1.171428571 – 0.7) / [0.249761791/sqrt(7)]

Test statistic = t = 4.9939

P-value = 0.0012

= 0.01

P-value < = 0.01

So, we reject the null hypothesis that the mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is 0.7 seconds.

There is sufficient evidence to conclude that the mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is greater than 0.7 seconds.

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