
For Problems 7-21, please provide the following information.
(a) What is the level of significance? Stale the null and alternate hypotheses, (b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain Compute the value of the sample test statistic and corresponding z value. (c) Find the P-value of the test statistic Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on sour answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistic ally significant at level a?
(c) Interpret your conclusion in the context of the application.
Focus Problem: Benford's Law Again, suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank (see Problem 7). You draw a random sample of n = 228 numbers from this file, and r = 92 have a first nonzero digit of 1.
Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.
i.Test the claim that p is more than 0.301. Use
ii.If p is in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1s. Could this indicate that the books have been “cooked" by artificially lowering numbers in the file? Comment from the point of view of the Internal Revenue Service, Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" by unscrupulous employees.
iii.Comment on the following statement: "If we reject the null hypothesis at level of significance
(i)
(a)

The level of significance, null and alternative hypothesis.
Answer to Problem 8P
Solution: The level of significance is
Explanation of Solution
The level of significance is defined as the probability of rejecting the null hypothesis when it is true, it is denoted by
Null hypothesis
Alternative hypothesis
(b)

To find: The sampling distribution that should be used and compute the z value of the sample test statistic.
Answer to Problem 8P
Solution: The sampling distribution
Explanation of Solution
Calculation:
The
The standardized sample test statistic for
(c)

To find: The P-value of the test statistic and sketch the sampling distribution showing the area corresponding to the P-value.
Answer to Problem 8P
Solution: The P-value of the test statistic is 0.0004.
Explanation of Solution
Calculation:
We have z = 3.37
Using Table 3 from the Appendix to find the specified area:
Thus P- value is 0.0004.
Graph:
To draw the required graphs using the Minitab, follow the below instructions:
Step 1: Go to the Minitab software.
Step 2: Go to Graph > Probability distribution plot > View probability.
Step 3: Select ‘Normal’ and enter Mean 0 and Standard deviation 1.
Step 4: Click on the Shaded area > X value.
Step 5: Enter X-value as 3.37 and select ‘Right tail’.
Step 6: Click on OK.
The obtained distribution graph is:
(d)

Whether we reject or fail to reject the null hypothesisand whether the data is statistically significant for a level of significance of 0.01.
Answer to Problem 8P
Solution: The P-value
Explanation of Solution
The P-value of 0.0004 is less than the level of significance (
(e)

The interpretation for the conclusion.
Answer to Problem 8P
Solution: There is sufficient evidence to conclude that population proportion of numbers with leading “1” in the revenue file is more than the probability 0.301.
Explanation of Solution
The P-value of 0.0004 is less than the level of significance (
(ii)

To explain: Whether it is suspect that there are too many numbers in the data file with leading 1's.
Answer to Problem 8P
Solution: Yes. The revenue data file seems to be too many entries with leading digit 1.
Explanation of Solution
There are too many numbers in the data file with leading 1's. So, we cannot say that it is an indication of the books have been “cooked” by artificially lowering numbers in the file. From the viewpoint of the Internal Revenue Service and the Federal Bureau of Investigation as it looks for “profit skimming”, it may be true or false because there are too many numbers in the data file with leading 1’s.
(iii)

To explain: Whether it recommends further investigation before accusing the company of fraud.
Answer to Problem 8P
Solution: Our data lead us to reject the null hypothesis, more investigation is merited.
Explanation of Solution
Since, we reject the null hypothesis
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Chapter 9 Solutions
UNDERSTANDING BASIC STATISTICS (LOOSE)
- The accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…arrow_forwardThe accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year Fossil Fuels Production Fossil Fuels Consumption Total Energy Consumption1949 28.748 29.002 31.9821950 32.563 31.632 34.6161951 35.792 34.008 36.9741952 34.977 33.800 36.7481953 35.349 34.826 37.6641954 33.764 33.877 36.6391955 37.364 37.410 40.2081956 39.771 38.888 41.7541957 40.133 38.926 41.7871958 37.216 38.717 41.6451959 39.045 40.550 43.4661960 39.869 42.137 45.0861961 40.307 42.758 45.7381962 41.732 44.681 47.8261963 44.037 46.509 49.6441964 45.789 48.543 51.8151965 47.235 50.577 54.0151966 50.035 53.514 57.0141967 52.597 55.127 58.9051968 54.306 58.502 62.4151969 56.286…arrow_forwardThe accompanying data shows the fossil fuels production, fossil fuels consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Develop line charts for each variable and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). What is the line chart for the variable Fossil Fuels Production?arrow_forward
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