300 people were interviewed and asked which genre of books they mostly read. The results are given below in a table of observed frequencies, classified by age.

Age

amp;

amp;

amp;0-25years

amp;26-50years

amp;51+years

amp;Totals

amp;

amp;Fiction

amp;23

amp;54

amp;29

amp;106

amp;Genre

amp;Non-fiction

amp;16

amp;38

amp;43

amp;97

amp;

amp;Sciencefiction

amp;41

amp;38

amp;18

amp;97

amp;

amp;Totals

amp;80

amp;130

amp;90

amp;300

\begin{matrix}\text{ } & \text{ } & \text{ } & \text{Genre} & \text{ } & \text{ }\\ \text{ } & \text{ } & \text{Fiction} & \text{Non-fiction} & \text{Science fiction} & \text{Totals}\\ \text{ } & \text{0-25 years} & \text{23} & \text{16} & \text{41} & \text{80}\\ \text{Age} & \text{26-50 years} & \text{54} & \text{38} & \text{38} & \text{130}\\ \text{ } & \text{51+ years} & \text{29} & \text{43} & \text{18} & \text{90}\\ \text{ } & \text{Totals} & \text{106} & \text{97} & \text{97} & \text{300}\\ \end{matrix}

Age

amp;

amp;

amp;0-25years

amp;26-50years

amp;51+years

amp;Totals

amp;

amp;Fiction

amp;23

amp;54

amp;29

amp;106

amp;Genre

amp;Non-fiction

amp;16

amp;38

amp;43

amp;97

amp;

amp;Sciencefiction

amp;41

amp;38

amp;18

amp;97

amp;

amp;Totals

amp;80

amp;130

amp;90

amp;300

Perform a

2

\chi^{2}

2

test, at the 5% significance level, to determine whether genre of book is independent of age. a. State the null hypothesis and the alternative hypothesis. b. Show that the expected frequency for science fiction and the 26-50 age group is 42. c. Write down the number of degrees of freedom. d. Write down the

2

calc

\chi_{\text {calc }}^{2}

calc

2

value for this data. The critical value is 9.488. e. Using the critical value or the p-value, comment on your result.