Hypothesis Testing

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  • Sale! z test

    A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. the mean score

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    Question: a study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. the mean score on the final exam for a course using the old edition is 75. ten randomly selected people who used the new text take the final exam their scores are shown.
    person: A,B,C,D,E,F,G,H,I,J
    score: 90,74,96,95,89,71,80,86,67,78
    Use a 0.01significance level to test the claim that people do better with the new edition. Assume the standard deviation is 10.5. ( Note you may wish to use statistical software).
    A.)what kind of test should be used?
    1. two-sided tail
    2. one tailed
    3. it does not matter
    B.) the test statistic is (rounded to two decimals)
    C.) the P-value is
    D.) is there sufficient evidence to support the claim that people do better than 75 on this exam? Y/N
    E.) construct a 99% confidence interval for the mean score for students using the new text. ____<mean<____

  • Sale! Hypothesis testing for proportion

    An opinion poll asks a simple random sample of 200 United States immigrants how they view their job prospects. In all, 121 say “good.” Does the poll give

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    An opinion poll asks a simple random sample of 200 United States immigrants how they view their job prospects. In all, 121 say “good.” Does the poll give convincing evidence to conclude that more than half of all immigrants think their job prospects are good? If P “the proportion of all immigrants who say their job prospects are good, what are the hypotheses for a test to answer this question.

  • Sale! Chi-square test

    A machine that fills cans of Mountain Lightning is supposed to put 12 ounces of beverage in each can. The variance of the amount in each can is 0.01.

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    Question: A machine that fills cans of Mountain Lightning is supposed to put 12 ounces of beverage in each can. The variance of the amount in each can is 0.01. The machine is moved to a new location, which has previously been shown to alter the machine settings. Determine whether the variance has changed following the move based on the following sample of the fills of 10 Mountain Lightning cans.
    12.18 11.77 12.09 12.03 11.87 11.96 12.03 12.36 12.28 11.85

  • Sale!

    A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when

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    Question: A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when the production process is working correctly. Based on past experience, the population standard deviation of the lifetime of the tires is 3,500 miles. Assume a level of significance for testing of 5%, and a random sample of 100 tires:
    A) What would be the consequences of making a Type II error in this problem?
    B) Compute the Probability of making a Type II error if the true population mean is 24,000 miles

  • Sale!

    Ben is interested in flirting. He wants to know what kinds of people

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    Question: Ben is interested in flirting. He wants to know what kinds of people are likely to be good (and bad) at flirting. He thinks that self-confidence will be correlated with flirting ability, but he’s not sure which way it will go. High self-confidence should make for good flirters, but if people are too self-confident, it might hurt their flirting performance. So he gives a number of students a self-confidence measure (Y) and then watches them try to flirt with people at an off-campus bar (X). Both scales range from 1 (low) to 7 (high). He records the following scores:

    Self-Confidence (X) Flirting (Y)
    4 5
    6 3
    6 5
    7 6
    6 7
    3 1
    6 4
    2 3
    3 2
    3 4
    1. a) Compute the correlation for these scores. (SHOW YOUR WORK! Use as much space as necessary.)
    2. b) What does this correlation tell us about the relationship between self-confidence and flirting ability?
    3. c) What is Ben’s alternative hypothesis?
    4. d) What is Ben’s null hypothesis?
    5. e) What is the coefficient of determination for these scores?
    6. f) How did you compute the coefficient of determination?
    7. g) How many degrees of freedom are there in this example?
    8. h) How did you compute the degrees of freedom? Should Ben perform a one-tailed or two-tailed test?  Why?
    9. i) Assuming α = .05, what is the critical value for this example?
    10. j) Is the correlation you computed statistically significant? YES  or   NO
    11. k) How do you know whether or not the correlation is statistically significant?
  • Sale! z test

    Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes. The franchise has installed

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    Question : Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

  • Sale! z test

    A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma

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    Question :  Hypothesis Testing

    A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma was $520. Suppose you would like to determine if the average weekly pay for all working women is significantly greater than that for women with a high school diploma. Data providing the weekly pay for a sample of 50 working women are available in the Excel file (Weekly Pay). Formulate the null and alternative hypotheses and conduct the appropriate test. What is your conclusion?

    Weekly Pay

    582         320       290     542     678       596        760         565        772

    333         685       800     619     697       557        804         687        691

    759         599       696     950     750       657         675        498

    633         753       627     614     569       617         736        712

    629         553       679     548     679      1230        565        533

    523         641       667     570     598       648         587        424

  • Sale! Chi-square goodness of fit test

    A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.13, 0.16, 0.13, and 0.58, respectively, from the least to most expensive variety.

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    Question: A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.13, 0.16, 0.13, and 0.58, respectively, from the least to most expensive variety. A sample of 482 purchases resulted in sales of 46, 151, 88, and 197 of the respective qualities. Does this sample contradict the expected proportions? Use α = .05.

    (a) Find the test statistic. (Give your answer correct to two decimal places.)

    (b) Find the p-value. (Give your answer bounds exactly.)
    ____< p < ____

  • Sale! Chi-square goodness of fit test

    A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9.

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    Question: A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers were as follows. At the 0.05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

    Integer 0 1 2 3 4 5 6 7 8 9
    Frequency 12 6 8 8 14 10 6 12 13 11

    (a) Find the test statistic. (Round your answer to two decimal places.)

    (b) Find the p-value. (Round your answer to four decimal places.)

  • Sale! z test

    Congress regulates corporate fuel economy and sets an annual gas mileage for cars.

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    Question:  Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to meet the goal of 30.4 mpg or better for their fleet of cars. To see if the goal is being​met, they check the gasoline usage for 46 company trips chosen at ​random, finding a mean of 31.4 mpg and a standard deviation of 2.57 mpg. Is this strong evidence that they have attained their fuel economy​ goal? Use 0.05 as the​ level of significance. p-Value = 0.006. State an appropriate conclusion. Choose the correct answer below.

  • Sale! Chi-square test

    A random sample of size 12 from a normal population is given below. 69 74 75 76 78 79 81 83 83 85 86 87

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    Question: A random sample of size 12 from a normal population is given below.
    69 74 75 76 78 79 81 83 83 85 86 87
    a) Someone claimed that s = 10. Does this data set support the claim? Test at a = 0.05.
    b) Test if the population mean is 85 using a = 0.05.
    c) Find the p-value of the test

  • Sale! z test

    Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes

    $2.00 $1.00

    Question:

    Last month the waiting time at the drive-through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

  • Sale! z test

    The life in hours of an electronic sensor is known to be approximately Normally distributed

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    Question:

    The life in hours of an electronic sensor is known to be approximately Normally distributed, with population standard deviation  = \sigma = 20 hours. A random sample of 10 sensors resulted in the following data: 500,550,560,575,525,505,510,540,550,545.

    • Is there evidence to support the claim that mean life exceeds 520 hours? Use a fixed-level test with alpha = 0.05.
    • What is the P-value of this test? Conclude the same of part (a)?
    • What is the Beta-value for this test if the true mean life is 535 hours?
    • What sample size would be required to ensure that Beta does not exceed 0.10 if the true mean life is 540 hours?
    • Construct a 95% one-sided lower CI on the mean life.
    • Use the CI found in part e) to test the hypothesis.
  • Sale! Chi-square test

    A manufacturer would like to determine if the variance in a product dimension exceeds 10

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    Question:

    A manufacturer would like to determine if the variance in a product dimension exceeds 10.

    a) State the Hypothesis to show the variance is greater than 10.

    b) Choose a level of a Use a= 0.05 for this problem.

    c) To test the hypothesis, the manufacturer takes a sample of 18 parts and measure that product dimension. The data appear in the Dimension worksheet of the HW3 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis.

    d) Sketch the sampling distribution. Include the critical value and test statistic.

    e) Draw a conclusion and report that in the problem context.

    f) What is the p-value for the hypothesis test?

    Part 1 2 3 4 5 6 7 8 9
    Data 48.3 48.5 54 49.3 48.8 56.6 45.8 55.2 45
    Part 10 11 12 13 14 15 16 17 18
    Data 52 46.4 51.2 50.4 47.6 45.1 44.8 44.9 56.3

     

  • Sale! Hypothesis testing for proportion

    Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach

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    Question

    Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that greater than 58% of those with diabetes who undergo this surgery will recover from diabetes? Use the a = 0.10 level of significance and the P-value method with the TI-84 calculator. Source: New England Journal of Medicine 357:753-761

    State the null and alternate hypotheses.

    Но: р (select)______

     H1 p (select) ______

    This hypothesis test is a (select) test