Question

Let's assume that the average length of all commercials aired on Hulu is 78 seconds. From a sample of 46 commercials aired during sitcoms, it was found that the average length of those commercials was 76 seconds with a standard deviation of 6.1 seconds. At the 5% significance level, does this data provide sufficient evidence to conclude that the mean length of sitcom commercials is different from 78 seconds?

Step 1: Stating what we are testing Step 2: Stating H₀, H_a, and alpha (α) Step 3: Stating the assumptions of the procedureStep 4: Stating whether we are using a z or t procedure and why

Step 5: Providing calculator output (make sure to include all the numbers mentioned in the template in the notes) Step 6: Interpreting results

Step 7: Stating what type of error we would be making and what it means Step 8: Stating the power of the test

Answer 1

Solution:

Step 1

Here, we are testing whether the mean length of sitcom commercials is different from 78 seconds.

Step 2

Null hypothesis: H₀: The mean length of sitcom commercials is 78 seconds.

Alternative hypothesis: H_a: The mean length of sitcom commercials is different from 78 seconds.

H₀: µ = 78 versus H_a: µ ≠ 78

This is a two tailed test.

Level of significance = 5% = α = 0.05

Step 3

Assumptions:

Data is a random sample.

Data is taken from normally distributed population.

Step 4

Here, we have to use t procedure because we are not given the value for the population standard deviation.

Step 5

The formula for test statistic is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

We are given

Xbar = 76

S = 6.1

n = 46

df = n – 1 = 46 – 1 = 45

t = (76 – 78)/[6.1/sqrt(46)]

t = -2/0.899396

t = -2.22371

P-value = 0.031231

(by using Ti-84 calculator or excel or t-table)

Step 6

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean length of sitcom commercials is different from 78 seconds.

Step 7

For this scenario, we are making type I error, it means the possibility of rejecting null hypothesis that mean length of sitcom commercials is 78 seconds, but in fact it is 78 seconds.

Step 8

The power of the test by using excel is given as 0.343.