Question

Question 5 a-e

Q5. The Dream Star Foundation used a survey to determine if the selection of a TV station is independent of the level of education (DreamWeek , January 25, 1982). From a poll of 800 television viewers, the following data have been obtained as to their levels of education and their preference of television stations. We are interested in determining if the selection of a TV station is independent of the level of education. Educational Level Television stations High School Bachelor Graduate TOTAL Public Broadcasting 50 150 80 280 Commercial Stations 150 250 120 520 TOTAL 200 400 200 800 a) (2pt) State the null and alternative hypotheses. b) (opt) Calculate the expected frequency. Show your work for full credit. c) (4pt) Compute chi-square statistic (x2). Show your work for full credit. d) (3pt) Find the degrees of freedom and the table value from the chi-square. Show your work for full credit. e) (3pt) Draw your conclusion. State your conclusion in a complete sentence and use words a non-statistician would understand. Show your work for full credit.

Answer 1

Observed,

Television stations	Educational level	Total
High School	Bachelor	Graduate
Public Broadcasting	50	150	80	280
Commercial station	150	250	120	520
Total	200	400	200	800

a) The null and alternative hypothesis are,

H₀ : Television Stations and Educational level are independent of each other.

H_a : Television Stations and Educational level are not independent of each other.

b) Expected Frequency

Television stations	Educational level	Total
High School	Bachelor	Graduate
Public Broadcasting	70	140	70	280
Commercial station	130	260	130	520
Total	200	400	200	800

c) Test statistics is,

$\small \chi^{2}=\sum \frac{(O-E)^{2}}{E}$

Television stations	Educational level	Total
High School	Bachelor	Graduate
Public Broadcasting	5.714	0.714	1.429	7.857
Commercial station	3.077	0.385	0.769	4.231
Total		12.088

d) Degrees of freedom = (3-1)*(2-1) = 2

Chi-square value,

$\small \chi^{2}_{0.05,2}= 5.99$

  $\small \chi^{2}_{0.01,2}= 9.21$

  $\small \chi^{2}_{0.10,2}= 4.61$

e) Conclusion,

We reject the null hypothesis, i.e. We conclude Television Stations and Educational level are not independent of each other.

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