In a survey of 450 adults 18 to 29 years of age, 419 said they use the Internet. In a survey of 400 adults 30 to 49 years of age, 324 said they use the internet. At a=0.01, can you reject the claim that the proportion of internet users is the same for two age groups?

Comparing the p value with the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the two proportions are different at 1% of significance

Step-by-step explanation:

Data given and notation  

represent the number of adults that use internet between 18-29 years

represent the number of adults that use internet between 30-49 years

sample selected

sample selected

represent the proportion of adults that use internet between 18-29 years

represent the proportion of adults that use internet between 30-49 years

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)  

significance level given

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We need to apply a z test to compare proportions, and the statistic is given by:  

  (1)  

Where  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

Statistical decision

Since is a two sided test the p value would be:  

Comparing the p value with the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the two proportions are different at 1% of significance

99

step-by-step explanation: