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In the past, 44% of those taking a public accounting-qualifying

By Gordon Grant,2014-04-29 19:39
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In the past, 44% of those taking a public accounting-qualifying

    ACCOUNTING QUALIFYING EXAMS

    Math 116 Reviewing for the Final Exam

    This is all about Proportions

Chapter 5 Binomial Probabilities

    1) In the past, 44% of those taking a public accounting-qualifying exam have passed the exam on their first try.

    a) Describe in words the population.

    b) Describe in words the success attribute.

    c) In a simple random sample of 250 applicants, what is the mean and standard deviation of

    the number of applicants who passed the exam on their first attempt? Round to one

    decimal place.

    d) Explain why this is a binomial experiment.

    e) Use the range rule of thumb to determine usual and unusual results for this experiment.

    f) In a simple random sample of 250 applicants, 130 passed on their first attempt. Is this

    result unusual?

    g) What could this result be suggesting?

    h) Assuming that 44% pass the exam on the first try, what is the probability that in a sample

    of 250 applicants, at least 130 passed on their first attempt?

    i) Use the probability rule to classify 130 as usual or unusual.

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    ACCOUNTING QUALIFYING EXAMS

    Chapter 6 Section 6.4 - Normal Approximation to a Binomial Distribution

    2) In the past, 44% of those taking a public accounting-qualifying exam have passed the exam on their first try. In a sample of 250 recent applicants, we observe that 130 of them passed on their first attempt. Assuming that 44% of those taking the test pass on their first try, what is the probability that in a group of 250 applicants at least 130 of them pass the exam on their first attempt? Use the normal distribution to estimate the answer. First make sure you verify that it is appropriate to use the normal distribution. What is this probability suggesting about the percentage of applicants who pass on their first attempt?

    (Comment: for large n, the continuity correction factor may not be necessary)

    ; Verify that the normal distribution is appropriate

    ; Find the mean and standard deviation of the binomial distribution

    ; Find the probability using the continuity correction factor

    With a calculator feature

     Showing all steps

    ; Complete the following:

    The probability that in groups of 250; 130 or more applicants pass on their first try is

    _________. This means, in 1000 trials of this experiment we expect about _____ trials to

    result in 130 or more passing on the first try. Because this event only happens 5 out of

    1000 times, we consider it to be unusual.

    ; What is this probability suggesting about the percentage of applicants who pass

    on their first attempt?

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    ACCOUNTING QUALIFYING EXAMS

    Chapter 7 Section 7.3 - Distribution of Sample Proportions

    3) 44% of those taking a public accounting qualifying exam pass the exam on their first try.

    a) Give the shape, mean and standard deviation of the distribution of sample proportions for samples of size 250.

    b) What is the probability that in a group of 250 applicants at least 52% of them pass the exam

    Note: If n is large, the continuity correction on their first attempt? What is this result suggesting?

    for p-hat won’t change the x interval much. Since we’ll be dealing with large n, we will not use it in the calculations in this section.

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    ACCOUNTING QUALIFYING EXAMS

    Chapter 8 Confidence Intervals about a Population Proportion

    4) A researcher wishes to estimate the percentage of applicants who take a public accounting qualifying exam and pass the test on their first try. He selects a sample of 250 applicants and observes that 130 of them passed on their first attempt.

    a) Determine the point estimate.

    b) Verify that the requirements for constructing a confidence interval about p-hat are

    satisfied.

    c) Construct a 90% confidence interval estimate for the percentage of applicants who pass

    on their first try.

    d) We are _____% confident that the true percentage of applicants who take a public

    accounting qualifying exam and pass the test on their first try is between _________%

    and __________%

    e) With ______% confidence we can say that ________% of people who take a public

    accounting exam pass the test on their first try with a margin of error of ________%

    f) The statement “90% confident” means that, if 100 samples of size _____ were taken,

    about _____ of the intervals will contain the parameter p and about ____ will not.

    g) In the past, 44% of those taking a public accounting-qualifying exam have passed the

    exam on their first try. Does the interval suggest that nowadays the percentage is still

    44%? Must explain.

    h) Section 8.4 - How many more applicants should be included in the sample to be 90%

    confident that a point estimate p-hat will be within 3% of p? Use a p-hat of 0.52.

    i) Section 8.4 - If no preliminary sample is taken to estimate p, how large a sample is

    necessary to be 90% confident that the point estimate p-hat will be within a distance of

    0.03 from p?

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    ACCOUNTING QUALIFYING EXAMS

    Chapter 9 Testing a Proportion p

    5) In the past, 44% of those taking a public accounting-qualifying exam have passed the exam on their first try. Lately, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his or her first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, can we conclude that the proportion passing on the first try has increased?