/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 According to a 2017 report, \(64... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 8

According to a 2017 report, \(64 \%\) of college graduate in Illinois had student loans. Suppose a random sample of 80 college graduates in Illinois is selected and 48 of them had student loans. (Source: Lendedu.com) a. What is the observed frequency of college graduates in the sample who had student loans? b. What is the observed proportion of college graduates in the sample who had student loans? c. What is the expected number of college graduates in the sample to have student loans if \(64 \%\) is the correct rate? Do not round off.

Short Answer

Expert verified
a. The observed frequency of college graduates with student loans is 48. \nb. The observed proportion of college graduates with student loans is 0.6 or 60%. \nc. The expected number of college graduates with student loans if 64% is the correct rate is 51.2.

Step by step solution

01

Calculate Observed Frequency

The observed frequency refers to the actual number of occurrences of an event. In this case, it is the number of graduates with student loans from the sample. According to the exercise statement, out of 80 college graduates selected, 48 had student loans. Therefore, the observed frequency is 48.
02

Calculate Observed Proportion

The observed proportion is the ratio of the number of occurrences of the event to the total sample size, expressed as a decimal or fraction. In this scenario, it would be the number of graduates with student loans divided by the total sample size. This is calculated as \(48 梅 80 = 0.6 \) or \(60\%\). Therefore, the observed proportion of graduates with student loans is 60%.
03

Calculate Expected Number

The expected number in statistical analysis refers to the number of times an outcome would be expected to occur based on a probability percentage. It is generally calculated by multiplying the total sample size by the probability. Here, it would be the total sample size (80) multiplied by the given rate (64%), expressed as a decimal. \( 80 * 0.64 = 51.2 \) Hence, the expected number of graduates with student loans, given a rate of 64%, is 51.2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Montreal, Canada, an experiment was done with parents of children who were thought to have a high risk of committing crimes when they became teenagers (Tremblay et al., 1996 ). Some of the families were randomly assigned to receive parental training, and the others were not. Out of 43 children whose parents were randomly assigned to the parental training group, 6 had been arrested by the age of \(15 .\) Out of 123 children whose parents were not in the parental training group, 37 had been arrested by age 15 . a. Find and compare the percentages of children arrested by age \(15 .\) Is this what researchers might have hoped? b. Create a two-way table from the data, and test whether the treatment program is associated with arrests. Use a significance level of \(0.05\). c. Do a two-proportion \(z\) -test, testing whether the parental training lowers the rate of bad results. Use a significance level of \(0.05\). d. Explain the difference in the results of the chi-square test and the twoproportion \(z\) -test. e. Can you conclude that the treatment causes the better result? Why or why not?

According to the website MedicalNewsToday.com, coronary artery disease accounts for about \(40 \%\) of deaths in the United States. Many people believe this is due to modern-day factors such as high-calorie fast food and lack of exercise. However, a study published in the Journal of the American Medical Association in November 2009 (www.medicalnewstoday .com) reported on 16 mummies from the Egyptian National Museum of Antiquities in Cairo. The mummies were examined, and 9 of them had hardening of the arteries, which seems to suggest that hardening of the arteries is not a new problem. a. Calculate the expected number of mummies with artery disease (assuming the rate is the same as in the modern day). Then calculate the expected number of mummies without artery disease (the rest). b. Calculate the observed value of the chi-square statistic for these mummies.

In a 2015 study by Nanney et al. and published in the Journal of American College Health, a random sample of community college students was asked whether they ate breakfast 3 or more times weekly. The data are reported by gender in the table. $$\begin{array}{lcc}\text { Eat breakfast at least } 3 \times \text { weekly } & \text { Females } & \text { Males } \\\\\hline \text { Yes } & 206 & 94 \\\\\text { No } & 92 & 49 \\\\\hline\end{array}$$ a. Find the row, column, and grand totals, and prepare a table showing these values as well as the counts given. b. Find the percentage of students overall who eat breakfast at least three times weekly. Round off to one decimal place. c. Find the expected number who eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. d. Find the expected number who did not eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. e. Calculate the observed value of the chi-square statistic.

There is a theory that relative finger length depends on testosterone level. The table shows a summary of the outcomes of an observational study that one of the authors carried out to determine whether men or women were more likely to have a ring finger that appeared longer than their index finger. Identify both of the variables, and state whether they are numerical or categorical. If numerical, state whether they are continuous or discrete. $$\begin{array}{|lcc|}\hline & \text { Men } & \text { Women } \\\\\hline \text { Ring Finger Longer } & 23 & 13 \\\\\hline \text { Ring Finger Not Longer } & 4 & 14 \\\\\hline\end{array}$$

According to the 2015 High School Youth Risk Behavior Survey, \(41.5 \%\) of high school students reported they had texted or emailed while driving a car or other vehicle. Suppose you randomly sample 80 high school students and ask if they have texted or emailed while driving. Suppose 38 say yes and 42 say no. Calculate the observed value of the chi-square statistic for testing the hypothesis that \(41.5 \%\) of high school students engage in this behavior.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.