# Short Response Checkpoint Lesson 15

411 Views
Votes

Short Response Checkpoint

Qn1.

Recently, a large music streaming service has taken steps to try to rid its "new music" recommendation algorithm of gender bias. Specifically, when suggesting a group of new artists to its users, the company's goal is for the gender distribution of the recommended artists to match the gender distribution of all artists on the streaming platform. Listed below are the proportion of all artists on the streaming service from each gender group (that the company collects information about):

 Gender Non-Binary Female Male Proportion 0.08 0.43 0.49

The company collects a random sample of 120 recommended artists from its new algorithm. Here is the gender information for the 120 sampled recommended artists:

 Gender Non-Binary Female Male 4 48 68

Perform a chi-squared test for goodness of fit to determine if the algorithm is truly making recommendations proportional to the total number of artists of each gender category on the streaming platform. Make sure to include the hypotheses, expected counts, degrees of freedom, chi-squared test statistic, p-value, and conclusion. Use a significance level of α = 0.05.

You may want to use the Chi-Squared Test tool to answer this question: https://dcmathpathways.shinyapps.io/ChiSquaredTest/

Qn2.

In the Pew Research Center's Core Trends survey that we discussed in the preview and in-class activity, respondents from a representative sample of American adults were asked how many books they read in the last year and whether or not they live in an urban, suburban, or rural area. The classifying counts for each category are given in the contingency table below.

 Type of Residence Type of Residence Type of Residence Urban Suburban Rural Number of Books None 133 144 81 Number of Books 1-4 146 149 53 Number of Books 5-9 76 74 33 Number of Books 10+ 194 216 76

Give the null and alternative hypotheses for a chi-squared test of independence for the variables number of books read and type of residence.

Qn3.

Suppose that an employee of the U.S. Department of Transportation is responsible for monitoring the bridges of the National Highway System in the neighboring states of New Jersey, New York, and Pennsylvania. Recent federal bridge maintenance in these three states should result in the same distribution of bridge conditions for all three states. This employee worries that this may not be the case and takes a random sample of bridges from each of the three states. The frequency of bridges in each sample found to be in good, fair, and poor condition are given in the two-way table below.

 Good Fair Poor New Jersey 26 87 7 New York 71 136 13 Pennsylvania 57 158 15

Conduct a chi-squared test of homogeneity at significance level 0.10 using the web app. You may want to use the Chi-Squared Test tool to answer this question: https://dcmathpathways.shinyapps.io/ChiSquaredTest/

a) Provide the hypotheses and conclusion of the hypothesis test.

b) As the federal employee responsible for monitoring the National Highway System bridges in these three states and ensuring that they maintain a similar distribution of bridge conditions, would you see a need to change your current plan of distributing bridge maintenance equally among the three states? Explain your answer in 1-2 sentences.