7. The Pew Research Center's Internet Project offers scholars access to raw data sets from their research. One of the Pew Research Center's projects was on teenagers and technology. A random sample of American families was selected to complete a questionnaire. For each of their children, between and including the ages of 13 and 15, parents of these families were asked: Do you know your child's password for any of [his/her] social media accounts?
Responses to this question were received from 493 families. The table below provides a summary of their responses.

1. A test for significance is to be undertaken to see whether there is an association between whether a parent knows any of their child's social media passwords and the age of the child.
   1. Clearly state the null and alternative hypotheses.
   2. Obtain the expected value that is missing from the table below, indicating clearly how it is calculated from the data values given in the table above. Expected values:

      	Age (years)
      Parent knows password	\(\mathbf { 1 3 }\)	\(\mathbf { 1 4 }\)	\(\mathbf { 1 5 }\)
      Yes	62.79	78.71	76.50
      No		99.29	96.50

   3. Obtain the two chi-squared contributions that are missing from the table below. Chi-squared contributions:

      	Age (years)
      Parent knows password	\(\mathbf { 1 3 }\)	\(\mathbf { 1 4 }\)	\(\mathbf { 1 5 }\)
      Yes		0.175	1.180
      No	2.203		0.935

      The following output was obtained from the statistical package that was used to undertake the analysis: $$\text { Pearson chi-squared } ( 2 ) = 7.409 \quad p \text {-value } = 0.0305$$
   4. Indicate how the degrees of freedom have been calculated for the chi-squared statistic.
   5. Interpret the output obtained from the statistical test in terms of the initial hypotheses.
2. Comment on the nature of the association observed, based on the contributions to the test statistic calculated in (a).