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 he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 73 said they bought a hard copy of the book, 30 said they printed it out from the web, and 23 said they read it online. (a) State the hypotheses for testing if the professor's predictions were inaccurate. (b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online? (c) This is an appropriate setting for a chi-square test. List the conditions required for a test and verify they are satisfied. (d) Calculate the chi-squared statistic, the degrees of freedom associated with it, and the p-value. (e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test? Interpret your conclusion in this context.

          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 he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 73 said they bought a hard copy of the book, 30 said they printed it out from the web, and 23 said they read it online.
(a) State the hypotheses for testing if the professor's predictions were inaccurate.
(b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online?
(c) This is an appropriate setting for a chi-square test. List the conditions required for a test and verify they are satisfied.
(d) Calculate the chi-squared statistic, the degrees of freedom associated with it, and the p-value.
(e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test? Interpret your conclusion in this context.

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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 he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 73 said they bought a hard copy of the book, 30 said they printed it out from the web, and 23 said they read it online.
(a) State the hypotheses for testing if the professor's predictions were inaccurate.
(b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online?
(c) This is an appropriate setting for a chi-square test. List the conditions required for a test and verify they are satisfied.
(d) Calculate the chi-squared statistic, the degrees of freedom associated with it, and the p-value.
(e) Based on the p-value calculated in part (d), what is the conclusion of the hypothesis test? Interpret your conclusion in this context.

Added by Scott B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Carolyn Behr-Jerome

08/12/2023

Step 1

The null hypothesis (H0) is that the professor's predictions are accurate, and the alternative hypothesis (H1) is that the professor's predictions are inaccurate. In terms of proportions, we can write this as: H0: p1 = 0.60, p2 = 0.25, p3 = 0.15 H1: At least one Show more…

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Transcript

00:01 So the first thing we need to do for this problem is we need to state our null and alternate hypothesis.

00:06 So our null hypothesis, i'm going to use, i'm going to type it out because it's a little easier to write it, easier to read, is that the population fits the specified distribution of categories.

00:32 So what the professor predicted for how the students read the book fits.

00:40 Our alternate hypothesis, then, is that the population does not fit or has a different distribution.

01:02 So what exactly did the professor predict? so 60 % of 126 is 75 .6.

01:12 So in this expected category, i'm not going to use 60%, i'll use 75 .6.

01:18 And then for those that printed a copy off the internet, he expected that to be 25 % of 126 students.

01:28 So that gives us 31 .5.

01:39 And then finally, those who read it online, he only expected it to be 15%, and that's 18 .9.

01:51 So what do i need to make sure this is a chi -squared test? so again, i'm going to type this out because it's a little easier.

01:59 So first, i need to make sure that each member of the population fits or can be classified into exactly one category.

02:28 So that's the case.

02:29 We do have that hard copy printed from the web, read online.

02:32 So that fits.

02:34 Second, we need a specified distribution with fixed probabilities.

02:46 And we do have that right here, 60%, 25%, 15%.

02:53 Next, a random sample, which we have because the students filled out a survey.

03:05 And then fourth, we have observed and expected values.

03:17 So next part, to find our chi -squared and our degrees of freedom and our p -value, i am going to use my calculator.

03:32 Now, the degrees of freedom, pretty easy to do.

03:35 Three categories subtract one, so that's two.

03:39 But with my calculator, i have to use the matrix capability...

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