Find the probability density function for U by using the method of transformations.

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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.

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Chapter 6.4, Problem 32E

To determine

Find the probability density function for U by using the method of transformations.

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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.

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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size). Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model. Interpret the…