Question

The director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds. He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds. He uses a significance level of 5%. What is the value of the test statistic?

Answer 1

The value of t test statistics is 4.518.

Explanation:

We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.

He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.

Let
`\mu` = mean length of commercials on his station.

So, Null Hypothesis,
`H_0` :
`\mu` = 24 seconds {means that the mean length of commercials on his station is equal to 24 seconds}

Alternate Hypothesis,
`H_A` :
`\mu\\eq` 24 seconds {means that the mean length of commercials on his station is different from 24 seconds}

The test statistics that would be used here 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 average length of these commercials = 26.3 seconds

s = sample standard deviation = 7.2 seconds

n = sample of commercials = 200

So, test statistics =
`(26.3-24)/((7.2)/(√(200) ) )` ~
`t_1_9_9`

= 4.518

The value of t test statistics is 4.518.