Question

An article titled "Teen Boys Forget Whatever It Was" appeared in the Australian newspaper The Mercury (April 21, 1997). It described a study of academic perfor- mance and attention span and reported that the mean time to distraction for teenage boys working on an inde- pendent task was 4 minutes. Although the sample size was not given in the article, suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 minutes. Is there convincing evidence that the average attention span for teenage boys is less than 5 minutes? Test the relevant hypotheses using a .01.

Answer 1

We conclude that the average attention span for teenage boys is less than 5 minutes.

Explanation:

We are given that the mean time to distraction for teenage boys working on an independent task was 4 minutes.

Suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 minutes.

Let
`\mu` = average attention span for teenage boys

SO, Null Hypothesis,
`H_0` :
`\mu \geq` 5 minutes {means that the average attention span for teenage boys is more than or equal to 5 minutes}

Alternate Hypothesis,
`H_A` :
`\mu` < 5 minutes {means that the average attention span for teenage boys is less than 5 minutes}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. =
`(\bar X -\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean attention time span for teenage boys = 4 min

s = sample standard deviation = 1.4 min

n = sample of teenage boys = 50

So, the test statistics =
`(4-5)/((1.4)/(√(50) ) )` ~
`t_4_9`

= -5.051

Now at 0.01 significance level, the t table gives critical value of -2.405 at 49 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -2.405 > -5.051, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average attention span for teenage boys is less than 5 minutes.