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8.8: Homework

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  • Use the following information to answer the next ten exercises. indicate which of the following choices best identifies the hypothesis test.

    1. independent group means, population standard deviations and/or variances known
    2. independent group means, population standard deviations and/or variances unknown
    3. matched or paired samples
    4. single mean
    5. two proportions
    6. 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 two pounds and three pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet.


    A new chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children who like the new chocolate bar is greater than the proportion of adults who 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 nine males and 16 females.


    A football league reported that the mean number of touchdowns per game was five. 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. One hundred 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 one year, respectively.


    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 a mean maternity-leave of six weeks.


    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. The following data are collected:

    Pre-course scorePost-course score

    Table 10.25


    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.


    Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown Table \(\PageIndex{26}\). Determine the appropriate test and best distribution to use for that test.

    Sample size4141
    Sample mean97.598.1
    Sample standard deviation17.519.2
    Table \(\PageIndex{26}\)
    1. Two independent means, normal distribution
    2. Two independent means, Student’s-t distribution
    3. Matched or paired samples, Student’s-t distribution
    4. Two population proportions, normal distribution

    A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four (4) new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as Table \(\PageIndex{27}\).

     Player 1Player 2Player 3Player 4
    Mean score before class83789387
    Mean score after class80808686
    Table \(\PageIndex{27}\)

    This is:

    1. a test of two independent means.
    2. a test of two proportions.
    3. a test of a single mean.
    4. a test of a single proportion.
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