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

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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.

     1

    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?

     2

    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.

     3

    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?

    ; Set both hypothesis

    ; Sketch graph, shade rejection region, label, and indicate possible locations of the

    point estimate in the graph.

    ****You should be wondering: Is p-hat = .52 higher than p = 0.44 by

    chance, or is it significantly higher? The p-value found below will help

    you in answering this.

    ; Use a feature of the calculator to test the hypothesis. Indicate the feature used and

    the results:

    Test statistic =

    p-value =

    ***How likely is it observing a p-hat =.52 or more when you select a

    sample of size 250 from a population that has a proportion of successes

    of 0.44?

     very likely, likely, unlikely, very unlikely

    *** Is p-hat = .52 higher than p = 0.44 by chance, or is it significantly

    higher?

    ; What is the initial conclusion with respect to Ho and H1?

    ; Write the conclusion using words from the problem

     5

    ACCOUNTING QUALIFYING EXAMS

    Chapters 8 and 9 Confidence Intervals and Hypothesis Testing about Two Population Proportions

    6) A public accounting qualifying exam was administered to both an experimental group and a control group after 6 weeks of instruction during which the experimental group received tutoring sessions and the control group did not. All 450 individuals were taking the exam for the first time and they were all using the same exam preparation books. The results of the experiment are:

     Sample size Passed on the first attempt

    Books and tutoring sessions 250 130

    Books and no tutoring 200 83

    sessions

    a) At the 5% significance level, can we conclude that the proportion of applicants who pass

    the accounting qualifying exam on the first try is higher in the group with tutoring

    sessions?

    ; Set both hypothesis

    ; Sketch graph, shade rejection region, label, and indicate possible locations of the

    point estimate in the graph.

    ****You should be wondering: Is the proportion of the group receiving

    tutoring sessions higher than that of the other group by chance, or is it

    significantly higher? The p-value found below will help you in

    answering this.

    ; Use a feature of the calculator to test the hypothesis. Indicate the feature used and

    the results:

    Test statistic =

    p-value =

    ***How likely is it observing such a difference or a more extreme one

    when you select samples from two populations that have the same

    proportions?

     very likely, likely, unlikely, very unlikely

    *** Higher by chance, or significantly higher?

    ; What is the initial conclusion with respect to Ho and H1?

    ; Write the conclusion using words from the problem

    b) Construct a 90% confidence interval estimate for the difference p1 p2 and interpret the

    results. What is the interval suggesting?

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