Question

**6.41 Open source textbook:** 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 he asks his 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.

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

- Ho: p
_{Buy}= .6, p_{Print}=.25, p_{Online}=.15

Ha: at least one of the claimed probabilities is different - Ho: p
_{Buy}= .6, p_{Print}=.25, p_{Online}=.15

Ha: at least one of the claimed probabilities is zero - Ho: p
_{Buy}= .6, p_{Print}=.25, p_{Online}=.15

Ha: all of the claimed probabilities are different

(b) How many students did the professor expect to buy the book,
print the book, and read the book exclusively online? *(please
do not round)*

Observed | Expected | |
---|---|---|

Buy Hard Copy | 71 | |

Print Out | 25 | |

Read Online | 15 |

(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: *(please round to four decimal places)* (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 do not have enough evidence to reject the null hypothesis
- Since p ≥ α we reject the null hypothesis and accept the alternative
- 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: pBuy = .6, pPrint=.25, pOnline=.15

Ha: at least one of the claimed probabilities is different

( b )

expect to buy the book = 111 * 0.6 = 66.6

expect to print the book = 111 * 0.25 = 27.75

expect to ead online = 111* 0.15 = 16.65

( c )

- chi-squared statistic = 0.727
- the degrees of freedom = 2
- p-value = 0.6952

Assuming alpha = 0.05

- Since p ≥ α we do not have enough evidence to reject the null hypothesis
- The data do not provide sufficient evidence to claim that the actual distribution differs from what the professor expected

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