State the hypotheses for testing if the professor's predictions were inaccurate. Ho: pBuy = .6, pPrint=.25, pOnline=.15 Ha: at least one of the claimed probabilities is different Ho: pBuy = .6, pPrint=.25, pOnline=.15 Ha: at least one of the claimed probabilities is zero Ho: pBuy = .6, pPrint=.25, pOnline=.15 Ha: all of the claimed probabilities are different Correct (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 75.6 Print Out 25 31.5 Read Online 15 18.9 (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) 2.32 (This is the correct answer, but I dont know how) I keep getting 2.43 or 2.426 The degrees of freedom associated with this test are: Correct The p-value associated with this test is: (please round to four decimal places) 0.3135 (Again, this is the correct answer) but I keep getting.2973 (e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test? Since p<α we fail to reject the null hypothesis 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 accept the null hypothesis Since p<α we reject the null hypothesis and accept the alternative Incorrect 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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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: pBuy = .6, pPrint=.25, pOnline=.15
Ha: at least one of the claimed probabilities is different - Ho: pBuy = .6, pPrint=.25, pOnline=.15
Ha: at least one of the claimed probabilities is zero - Ho: pBuy = .6, pPrint=.25, pOnline=.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 | 75.6 |
| Print Out | 25 | 31.5 |
| Read Online | 15 | 18.9 |
(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: Correct
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 fail to reject the null hypothesis
- 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 accept the null hypothesis
- Since p<α we reject the null hypothesis and accept the alternative
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
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