Question

1)

A professor using an open-source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. At the end of the semester she asks her students to complete a survey where they indicate what format of the book they used. Of the 126 students, 71 said they bought a hard copy of the book, 30 said they printed it out from the web, and 25 said they read it online. What would be the appropriate set of hypotheses for testing if the professor's predictions were accurate?

• H0: The actual proportion of students who purchase the hard copy of the book is 60%.

  HA: The actual proportion of students who purchase the hard copy of the book is higher than 60%.

• H0: The actual proportion of students who purchase the hard copy of the book is higher than 60%.

  HA: The actual proportion of students who purchase the hard copy of the book is lower than 60%.

• H0: The distribution of the format of the book used by the students does not follow the professor's predictions. HA: The distribution of the format of the book used by the students follows the professor's predictions.
• H0: The distribution of the format of the book used by the students follows the professor's predictions.

  HA: The distribution of the format of the book used by the students does not follow the professor's predictions.

2)

You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Category	Observed Frequency	Expected Frequency
A	12
B	20
C	8
D	25
E	6

Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.)
χ2=χ2=

What are the degrees of freedom for this test?
d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• accept the alternative

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• The sample data support the claim that all 5 categories are equally likely to be selected.
• There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

Answer 1

1)

H0: The distribution of the format of the book used by the students follows the professor's predictions.

HA: The distribution of the format of the book used by the students does not follow the professor's predictions.

2)

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
1	0.20	12.00	14.20	-0.58	0.341
2	0.20	20.00	14.20	1.54	2.369
3	0.20	8.00	14.20	-1.65	2.707
4	0.20	25.00	14.20	2.87	8.214
5	0.20	6.00	14.20	-2.18	4.735
total	1.000	71	71		18.3662
test statistic X2 =	18.366

degree of freedom =categories-1=

4

p value =

0.0010

The p-value is  less than alpha

reject the null

There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.