In: Statistics and Probability
3. In 2000, a sample of 209 people aged 18-30 found that they spent an average of 6.75 hrs/week on the internet. In 2006, a sample of 541 people aged 18-30 spent an average of 7.34 hrs/week on the internet. Has the average increased?
Use correct notation where appropriate.
For each of the following situations,
a) What is/are the population(s) in the study?
b) Does the scenario involve 1 or 2 parameters to be
estimated/tested/compared?
c) What is/are the parameter(s) to be estimated/tested/compared? Be
specific and use the appropriate notation.
d) What is/are the variable(s) involved. Is each numerical or
categorical?
e) Is it most appropriate to create a confidence interval or
conduct a hypothesis test? If a hypothesis test should be
conducted, state the
hypotheses.
f) Will the critical value or test statistic be a z-value or
t-value?
(a) The populations in study are the people aged 18 - 30 who spent on the internet in the years 2000 and 2006.
(b) The scenario involves 2 parameters to be compared.
(c) The parameters to be compared are p1, which is the proportion of people aged 18 - 30 who spent on the internet in 2000 and p2, the proportion of people 18-30 who spent on the internet in 2006. The comparison to be made is if p1 is > p2.
(d) The variables involved are
(i) Amount Spent - Numerical
(ii) The year in which it was spent - Categorical
(iii) The age group - Categorical.
(e) It is better to do a Hypothesis test as we are doing a right tailed test (CI is 2 tailed)
The Hypothesis is:
H0: p1 = p2: The proportion of people aged 18 - 30 who shopped on the internet in 2002 is equal to the proportion in 2006.
Ha: p1 > p2: The proportion of people aged 18 - 30 who shopped on the internet in 2002 is greater then the proportion of those in 2006.
(f) The critical value will be a z value, as the following conditions are met
(i) The sampling is random
(ii) The samples are independent of each other
(iii) n * , n * (1 - ), n * and n * (1 - ) are all greater than 10.