The he average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average.

1. State the null and alternative hypotheses to be tested.

2. Compute the test statistic.

3. The null hypothesis is to be tested at 95% confidence. What do you conclude?

a) Null hypothesis:  

Alternative hypothesis:  

b)  

c) The degrees of freedom are given by:

Now we can calculate the p value, since we are conducting a two tailed test:

Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

Step-by-step explanation:

Information provided

represent the sample mean   in minutes

represent the standard deviation

sample size  

represent the value to verify

represent the significance level

t would represent the statistic (variable of interest)  

represent the p value

Part a

We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Part b

Since we don't know the population deviation the statistic is given by:

(1)  

Replacing the info given we got:

Part c

The degrees of freedom are given by:

Now we can calculate the p value, since we are conducting a two tailed test:

Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes