9. Hypothesis Testing for One Sample

Credit ScoresA Fair Isaac Corporation (FICO) score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850, with a FICO score over 700 considered to be a quality credit risk. According to Fair Isaac Corporation, the mean FICO score is 703.5. A credit analyst wondered whether high-income individuals (incomes in excess of \$100,000 per year) had higher credit scores. He obtained a random sample of 40 high-income individuals and found the sample mean credit score to be 714.2 with a standard deviation of 83.2. Conduct the appropriate test to determine if high-income individuals have higher FICO scores at the α = 0.05 level of significance.

[DATA] Family Size A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows:

Note: x̄ = 2.27, s = 1.22.

a. What is the shape of the distribution of the sample mean? Why?

To test H0: μ = 100 versus H1: μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.

d. Will the researcher reject the null hypothesis? Why?

To test H0: μ = 100 versus H1: μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.

e. Construct a 99% confidence interval to test the hypothesis.

SAT Verbal ScoresDo students who learned English and another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English and another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical Reading exam?

a. State the appropriate null and alternative hypotheses.

SAT Verbal ScoresDo students who learned English and another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English and another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical Reading exam?

b. Verify that the requirements to perform the test using the t-distribution are satisfied.

SAT Verbal ScoresDo students who learned English and another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English and another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical Reading exam?

c. Use the classical or P-value approach at the α = 0.1 level of significance to test the hypotheses in part (a).

SAT Verbal ScoresDo students who learned English and another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English and another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical Reading exam?

d. Write a conclusion based on your results to part (c).

"[DATA] Starbucks StockThe volume of a stock is the number of shares traded for a given day. In 2011, Starbucks stock had a mean daily volume of 7.52 million shares according to Yahoo!Finance. A random sample of 40 trading days in 2018 was obtained and the volume of shares traded on those days was recorded. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 10_3_27 using the file format of your choice for the version of the text you are using.

d. Does the evidence suggest that the volume of Starbucks stock has changed since 2011? Use an α = 0.05 level of significance."

"SimulationSimulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15.

a. Test the null hypothesis H0: μ = 100 versus H1: μ ≠ 100 for each of the 100 simple random samples."

Explain the difference between statistical significance and practical significance.

"Course RedesignPass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of a community college develop a mastery-based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning mentor for the students. Of the 480 students who enroll in the mastery-based course, 267 pass.

a. What is the variable of interest in this study? What type of variable is it?"

"Course RedesignPass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of a community college develop a mastery-based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning mentor for the students. Of the 480 students who enroll in the mastery-based course, 267 pass.

c. Explain why a 0.01 level of significance might be used to test this hypothesis."

"In Problems 20–25, decide whether the problem requires a confidence interval or hypothesis test, and determine the variable of interest. For any problem requiring a confidence interval, state whether the confidence interval will be for a population proportion or population mean. For any problem requiring a hypothesis test, write the null and alternative hypothesis.

According to the Pew Research Center, 55% of adult Americans support the death penalty for those convicted of murder. A social scientist wondered whether a higher proportion of adult Americans with at least a bachelor’s degree support the death penalty for those convicted of murder."

"To test H0: mu = 100 versus Ha: mu > 100, a simple random sample of size n = 35 is obtained from an unknown distribution. The sample mean is 104.3 and the sample standard deviation is 12.4.

a. To use the t-distribution, why must the sample size be large?"