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Answer:
We conclude that the average attention span for teenage boys is less than 5 minutes.
Step-by-step 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.
<u><em>Let </em></u><u><em> = average attention span for teenage boys</em></u>
SO, Null Hypothesis, :
5 minutes {means that the average attention span for teenage boys is more than or equal to 5 minutes}
Alternate Hypothesis, :
< 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 <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean attention time span for teenage boys = 4 min
s = sample standard deviation = 1.4 min
n = sample of teenage boys = 50
So, <u><em>the test statistics</em></u> = ~
= -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, <u>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.</u>
Therefore, we conclude that the average attention span for teenage boys is less than 5 minutes.