Question

1. A professor using an open source introductory statistics book predicts that 10% of the students will purchase a hard copy of the book, 55% will print it out from the web, and 35% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 200 students, 25 said they bought a hard copy of the book, 85 said they printed it out from the web, and 90 said they read it online.

(a) State the hypotheses for testing if the professor's predictions were inaccurate.

• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: at least one of the claimed probabilities is different
• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: all of the claimed probabilities are different
• Ho: p_Buy = .1, p_Print=.55, p_Online=.35
  Ha: at least one of the claimed probabilities is zero

(b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online? (if necessary, round to the nearest whole number)

	Observed	Expected
Buy Hard Copy	25
Print Out	85
Read Online	90

(c) Calculate the chi-squared statistic, the degrees of freedom associated with it, and the p-value.

The value of the test-statistic is:  (please round to two decimal places)

The degrees of freedom associated with this test are:

The p-value associated with this test is:

• greater than .1
• less than .01
• between .05 and .1
• between .01 and .05

(e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test?

• Since p ≥ α we reject the null hypothesis and accept the alternative
• Since p<α we reject the null hypothesis and accept the alternative
• Since p ≥ α we do not have enough evidence to reject the null hypothesis
• Since p<α we fail to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis

Interpret your conclusion in this context.

• The data provide sufficient evidence to claim that the actual distribution differs from what the professor expected
• The data do not provide sufficient evidence to claim that the actual distribution differs from what the professor expected

Answer 1

a)

Ho: p_Buy = .1, p_Print=.55, p_Online=.35
Ha: at least one of the claimed probabilities is different

b)

since expected =np , where n=200

therefore

		observed	Expected
category		Oi	Ei=total*p
buy hard copy		25.0000	20.00
Print out		85.0000	110.00
red online		90.0000	70.00

c)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
buy hard copy	0.1000	25.0000	20.00	1.12	1.250
Print out	0.5500	85.0000	110.00	-2.38	5.682
red online	0.3500	90.0000	70.00	2.39	5.714
total	1.000	200	200		12.6461
test statistic X2 =		12.65

degree of freedom =categories-1=

2

p value =

0.0018

less than .01

e) Since p<α we reject the null hypothesis and accept the alternative

The data provide sufficient evidence to claim that the actual distribution differs from what the professor expected