### Statistical Analysis of Graduation Rates Among Women Athletes**Problem Statement:**Women athletes at a university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes from the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from this university has changed (either way)? Use a 5% level of significance.**Objective:**- To determine if the graduation rate of women athletes has significantly changed from the established rate of 67%.**Given Data:**- Long-term graduation rate (population proportion), $ p_0 $ = 67% or 0.67.- Sample size, $ n $ = 38.- Number of graduates in the sample, $ x $ = 21.- Sample proportion, $ \hat{p} $ = $ \frac{x}{n} $ = $ \frac{21}{38} $.**Hypotheses:**- Null Hypothesis, $ H_0 $: $ p = 0.67 $ (Graduation rate has not changed).- Alternative Hypothesis, $ H_1 $: $ p \neq 0.67 $ (Graduation rate has changed).**Level of Significance:**- $ \alpha $ = 0.05 (5%).**Test Statistic (z-score):**Use the formula for the z-score in a proportion test:\[ Z = \frac{\hat{p} - p_0}{ \sqrt{\frac{p_0 (1 - p_0)}{n}} } \]- Calculate $ \hat{p} $:\[ \hat{p} = \frac{21}{38} \approx 0.5526 \]- Calculate the standard error (SE):\[ SE = \sqrt{ \frac{0.67 \times (1 - 0.67)}{38} } \approx 0.0772 \]- Calculate the z-score:\[ Z = \frac{0.5526 - 0.67}{0.0772} \approx -1.521 \]**Decision Rule:**- Compare the calculated z-score with the critical z-value from the standard normal distribution table. For a two-tailed test at the 0.05 significance level, the critical z-values are approximately ±1.96.

Name: ### Statistical Analysis of Graduation Rates Among Women Athletes**Pr
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: ### Statistical Analysis of Graduation Rates Among Women Athletes**Problem Statement:**Women athletes at a university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes from the school showed t

Answered: Image /qna-images/answer/6bd923d4-7733-4072-85a2-3a19ed8ff61d.jpg

Math

Statistics

4. Women athletes at a university have a long term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from this university has changed (either way)? Use a 5% level of significance.

4. Women athletes at a university have a long term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from this university has changed (either way)? Use a 5% level of significance.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

To collect data about the amount of time students spend studying for exams, which of the following methods should a teacher use to lead to a sample that is the most representative of the students in the school? Survey all the students who are in their final year of high school. Survey all students who achieved over 85% on their report card last semester. Survey all the students who play football. Survey all the students in the classes that he or she teaches. Survey 20 randomly selected students from each grade.
Security scans are often completed on computers in a particular college to assess the security risk from viruses etc. A sample of 120 computers which are considered at risk for viruses and other security issues are checked with a particular security scanner on a Monday and then monitored over the following week. The number of computers which broke down over the following week were recorded. The results are as follows: Security Scan (% Risk) Breakdown No Breakdown Low Risk (0 - 10%) 3 61 Slight/Moderate Risk (10 – 30%) 13 28 High Risk (>30%) 12 3 (i) Based on the above sample work out the probability that a computer in the college will breakdown. Input your answer correct to 4 decimal places here: (ii) Based on the above sample work out the probability that a computer has a low risk level OR doesn't breakdown. Input your answer correct to 4 decimal places here: (iii) Based on the above sample work out the probability that a computer has a high risk AND has a breakdown. Input your answer…
The Wisconsin Fish and Game Department stocked a lake with 30% catfish, 15 % bass, 40% bluegill, and 15% Northern Pike. Five years later they took a random sample of 500 fish from the lake and found 120 catfish, 85 bass, 220 bluegill, and 75 Northern Pike. At the 5% level of significance, can we show that the distribution of fish changed over the 5-year interval? State and test appropriate hypotheses. State conclusions.
A researcher believes that there may be a negative association between the quantity of fertilizer used and the percentage of the population who live in rural areas in different countries. The data below shows the percentage of the population who live in rural areas and the fertilizer use measured in kg per hectare, for a random sample of 11 countries. 33%= 76kg, 6%=44kg, 58%= 6kg, 35%=68kg, 81%=3kg, 69%=10kg, 61%=7kg, 7%=176kg,74%=5kg, 71%=137kg, 17%=157kg Use the Spearman's rank order coefficient method to affirm or disagree with the researchers assumption.
A bank wonders if omitting the annual fee for customers who charge at least $4000 per year would increase the amount of credit card usage (i. e. the total amount charged in a year). The bank makes this offer to a random sample of customers that have spent at least $4000. It then compares how much these customers charged this year with how much they charged last year. This data is found on sheet "CC Fees." Is there evidence at a 5% significance level to state that the mean amount increases when the "no-fee" offer was given?
An auto shop wants to examine the proportion of customers that have to return after an appointment. Last year, an examination of 375 customers found that 26.9% had to return after an appointment. You instituted some changes at the auto shop this year, and found from a sample of 430 customers that 33.9% had to return after an appointment. You want to conduct an analysis to determine if there has been an increase in the proportion of customers that need to return after an appointment since the past year, with a significance level of 1%. Using this information, what is the test statistic of your analysis? For the purposes of this analysis, use - Pcurrent year Plast Round any intermediate numbers to four decimal year. places and choose the closest choice to your answer. 2.575 1.03 2.15 1.64 3.30
Which of these experimental designs has the most statistical power (is more likely to show a true difference between 2 treatment conditions)? A. Between-Subjects B. Descriptive Study C. Correlational Study D. Within-Subjects
A random sample of 1100 potential voters was randomly divided into 2 groups. Group 1: 500 potential voters; no registration reminders sent; 248 registered to vote Group 2: 600 potential voters; registration reminders sent; 332 registered to vote Do these data support the claim that the proportion of voters who registered was greater in the group that received reminders than in the group that did not? Use a 1% level of significance.
Primary seat belt laws allow police to stop a motorist for not wearing a seat belt. According to the National Highway Traffic Safety Administration, the percentage of drivers wearing seat belts in the Limpopo province was 68.5% in 2017 and 72% in 2018. Assume that these percentages are based on random samples of 1000 drivers in 2017 and 1050 in 2018. Suppose you must test at 5% level of significance whether the proportion of all drivers in Limpopo province who used seat belts in 2017 is lower than that for 2018. 1 Questions I) Determine the alternative hypothesis to be tested: II) Determine the value of test statistic: III) Determine the p-value for this problem: IV) the conclusion Since Z=-1.734 is greater than Z subscript 0.05 end subscript equals negative 1.645, we then reject the null hypothesis at 5% level of significance and conclude that the proportion of all drivers in Limpopo province who used seat belts in 2017 is lower than that for 2018. b) Since Z=-1.734 is less…
55% of home owners who received Notice of Violations letters from their HOA experienced anxiousness, 76% of home owners who received such letters experienced outrage, only 2% experienced neither of the two aforementioned effects. What is the percentage of home owners who experienced both effects?