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For questions [link] - [link] , indicate which of the following choices best identifies the hypothesis test.

  • Independent group means, population standard deviations and/or variances known
  • Independent group means, population standard deviations and/or variances unknown
  • Matched or paired samples
  • Single mean
  • 2 proportions
  • Single proportion

A powder diet is tested on 49 people and a liquid diet is tested on 36 different people. The population standard deviations are 2 pounds and 3 pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet.

A

A new chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children that like the new chocolate bar is greater thanthe proportion of adults that like it.

The mean number of English courses taken in a two–year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 9 males and 16 females.

B

A football league reported that the mean number of touchdowns per game was 5. A study is done to determine if the mean number of touchdowns has decreased.

A study is done to determine if students in the California state university system take longer to graduate than students enrolled in private universities. 100 students from both the California state university system and private universities are surveyed. From years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively.

A

According to a YWCA Rape Crisis Center newsletter, 75% of rape victims know their attackers. A study is done to verify this.

According to a recent study, U.S. companies have an mean maternity-leave of six weeks.

D

A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national percent. Suppose that a survey of 100 local youths and 100 national youths is conducted to see if the proportion of drug and alcohol use is higher locally than nationally.

A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. Of interest is the mean increase in SAT scores.

C

University of Michigan researchers reported in the Journal of the National Cancer Institute that quitting smoking is especially beneficial for those under age 49. In this American Cancer Society study, the risk (probability) of dying of lung cancer was about the same as for those who had never smoked.

For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in 14. Appendix (online book version: the link is "Solution Sheets"; PDF book version: look under 14.5 Solution Sheets). Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.
If you are using a student's-t distribution for a homework problem below, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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