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: pBuy = .1, pPrint=.55, pOnline=.35 Ha: at least one of the claimed probabilities is different Ho: pBuy = .1, pPrint=.55, pOnline=.35 Ha: at least one of the claimed probabilities is zero Ho: pBuy = .1, pPrint=.55, pOnline=.35 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? (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: less than .01 greater than .1 between .01 and .05 between .05 and .1 (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 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 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
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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: pBuy = .1, pPrint=.55, pOnline=.35
Ha: at least one of the claimed probabilities is different - Ho: pBuy = .1, pPrint=.55, pOnline=.35
Ha: at least one of the claimed probabilities is zero - Ho: pBuy = .1, pPrint=.55, pOnline=.35
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? (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:
- less than .01
- greater than .1
- between .01 and .05
- between .05 and .1
(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 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 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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