Answer True or False

1. A in a density histogram the area of a region is equivalent to the density of that region_________.
2. Extreme values or “outlier” have a great effect on the Interquartile range than on the standard deviation as the standard deviation is a resistant measure of spread_______.
3. In the events A and B are disjoint they must also be independent_______.
4. For any two events A and B, P (A or B)= P(B)+ P(A and B). ________.
5. If the events A and B are independent, the P (A and B) = P(A)P(B)_________.
6. If the events A and B are disjoint then conditional probabilities P(AB) and P(BA) are both equal to 0______.
7. A random variable that assumes only negative values will have a negative mean ______.
8. A random variable that assumes only negative values will have a negative standard deviation______.
9. A binomial random variable counts the number of “successes” in a fixed number of independent trials where the probability of “success” varies from trial to trial_____.
10. A statistic is a random quantity: different random samples will yield different statistic values______.
11. The mean of sampling distribution of the sample mean is equal to the population mean_____.
12. The standard deviation of the sampling distribution of the the sample mean is generally smaller than the standard deviation of the population_____.
13. If the population is (exactly) normally distributed, the sampling distribution of the sample mean will be (exactly) normal also______.
14. Even if the population distribution is not normal, as long as the sample size is sufficiently large, the sampling distribution of the sample mean will be approximately normal, by central limit theorem______.
15. A 95% Confidence Interval will generally be wider than a 90% Confidence Interval for the same parameter, based on the same data ______.  
16. A 95% Confidence Interval for a population mean will contain at least 95% of the values in the underlying population_______.
17. If we were to take a large number of independent random samples and calculate a A 95% Confidence Interval from about 95% of the resulting intervals would cover the true parameter value______.
18. In hypothesis testing, H₀is a statement about the population that we initially assume to be true________.
19. A P-value close to zero indicated that the observed data are inconsistent with the null hypothesis______.
20. If we reject H₀at the a=0.05 level of significance clearly we would reject a=0.01 as well_______.
21. A P-value less than 0.01 indicates that if H₀ were true, the chance of observing data as extreme as those observed would be less than one out of 100______.
22. In a two-way contingency table, the marginal (row and column) sums of the “expected cell counts” will be equivalent marginal sums of the observed cell counts_______.
23. Evidence against the null hypothesis of independent between row and column variables in a contingency table is provided by a very small value of the chi-square statistic_____.
24. In an r x c contingency table the P-value for a test of row-column is found by comparing the test statistic x^2 to the chi-square distribution with (r-1)(c-1) degrees of freedom______.
25. If two quantitative variable x and y are negatively associated above average values of x will tend to occur with below average values of y and vice versa_______.
26. If a set of data (x₁, y₁) ……. (x_n,y_n) satisfy y_i=4x for each i=1…n then the correlation between the x’s and the y’s is 1______.
27. Correlation is a resistant measure in that it is not sensitive to extreme values or outliers______.
28. Correlation makes a distinction between response variable and explanatory variable______.
29. Least-square regression makes a distinction between response variable and explanatory variable______.
30. The least square regression line always passes through the point(xbar, ybar) ______.

The data in tab #2 pertain to the years of experience of project managers and the numbers of successes and failures they have had on major projects. Use the data set given in tab #2 in the attached Excel workbook and logistic regression to find the following:

The probability of success given 10 years of experience is: .

The probability of failure given 18 years of experience is: .  

In the 2015 federal election, 39.5% of the electorate voted for the Liberal party, 31.9% for the Conservative party, 19.7% for the NDP, 4.7% for the Bloc Quebecois and 3.5% for the Green party. The most recent pool as of the launch of the 2019 election campaign shows a tie between the Liberals and the Conservatives at 33.8%. This pool was based on 1185 respondents.

(a) Based on this recent pool, test whether this is sufficient evidence to conclude that the level of support for the conservatives has increased since the last election. Use the 5% level of significance and show your manual calculations.

(b) Using recent pool data, build an appropriate 95% one-sided confidence interval for the true proportion of support for the conservatives. Is this CI consistent with your conclusion in a) above?

(c) Would your conclusion be the same as in a) above if you had used a 10% confidence level for the hypothesis test?

(d) Now, suppose you want to estimate the national level of support for the Liberals at the start of the 2019 campaign using a 95% 2-sided confidence interval with a margin of error of  1% based on the results of the last election, what sample size would be required

(e) Would the sample size calculated above be sufficient to estimate the support for the Bloc Quebecois within the same level of confidence and margin of error? If not, how many more respondents would you need?

A marksman's chance of hitting a target with each of his shots is 60%. (Assume the shots are independent of each other.) If he fires 30 shots, what is the probability of his hitting the target in each of the following situations? (Round your answers to four decimal places.) (a) at least 21 times (b) fewer than 13 times (c) between 14 and 21 times, inclusive

6. (a).

In a particular town 10% of the families have no children, 30% have one child, 20% have
two children, 40% have three children, and 0% have four. Let T represent the total
number of children, and G the number of girls, in a family chosen at random from this
town. Assuming that children are equally likely to be boys or girls, find the distribution
of G. Display your answer in a table and sketch the histogram.

(b). Find E(T | G=1) = conditional expectation of number of children T, given 1 girl.

(c). Find the sum over k= 0, , 2, 3 of

E (T | G=k) P( G= k).

HINT: The hard way is to compute both factors of all 4 terms and do the arithmetic. The easy way is to use the R.A.C.E.

tail1,tail2
11.5,4
5.3,4.4
9.2,7.9
10.1,9.9
6.3,6
8.2,6.4
9.9,4.3
7.8,8.8
7.9,7.6
8.9,1.5
8.2,4.9
7.2,5.7
8,4
12.1,5.7
10,3.9
6.5,6.9
5.8,6.9
7.6,7.8
11,7
8.9,9.4
6.9,5.4
10.1,1.9
8,6.3
6.1,7.5
9.2,5.4
11.3,9
9.2,8.4
8.7,7.3
7,6.3
9.4,5.1

Conduct a hypothesis test assessing if tail length for species 1 is greater than the tail length for species 2. Provide the R code necessary to conduct this test and interpret the results of the test using a test statistic

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who are confident with their​ country's banking system. His estimate must be accurate within 5​% of the population proportion. ​(a) No preliminary estimate is available. Find the minimum sample size needed. ​(b) Find the minimum sample size​ needed, using a prior study that found that 25​% of the respondents said they are confident with their​ country's banking system. ​(c) Compare the results from parts ​(a) and ​(b). ​(a) What is the minimum sample size needed assuming that no prior information is​ available?

agree or not?

What is a nonparametric test? What is a parametric analysis?

Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric analysis is reliable. The student’s t-test for two independent samples is safe only if each sample follows a normal distribution and if sample variances are homogeneous. Nonparametric tests do not rely on any delivery. They can thus be applied even if parametric conditions of validity are not met. Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid. 3.

what is the difference between a nonparametric test and a distribution-free test?

While nonparametric tests don’t assume that your data follow a normal distribution, they do have other assumptions that can be hard to meet. For nonparametric tests that compare groups, a common assumption is that the data for all groups must have the same spread dispersion. If your groups have a different spread, the nonparametric tests might not provide valid results. On the other hand, if you use the 2-sample t-test or One-Way ANOVA, you can simply go to the Options sub dialog and uncheck Assume equal variances. Voilà, you’re good to go even when the groups have different spreads.

6) Provide an example of counting in your everyday life. Think of an example where you could use a counting method and describe the method.

I'm having trouble applying bayes formula with the following multi-part question

In April 2013, the total sales from General Motors, Ford, or Chrysler was 606,334 cars or light trucks. The probability that the vehicle sold was made by General Motors was 0.392, by Ford 0.350, by Chrysler 0.258. Additionally, the probability that a General Motors vehicle sold was a car was 0.395, a Ford vehicle sold was a car was 0.370, and a Chrysler vehicle sold was a car was 0.332.

(1) Given the vehicle sold was a car, find the probability it was made by General Motors

(a) About 0.332 ; (b) About 0.274 ; (c) About 0.376 ; (d) About 0.232 ; (e) About 0.418 ;

(2) Given the vehicle sold was a car, find the probability it was made by Chrysler.

(a) About 0.376 ; (b) About 0.232 ; (c) About 0.332 ; (d) About 0.274 ; (e) About 0.418 ;

(3) Given the vehicle sold was a light truck, find the probability it was made by General Motors.

(a) About 0.418 ; (b) About 0.232 ; (c) About 0.376 ; (d) About 0.274 ; (e) About 0.332 ;

(4) Given the vehicle sold was a light truck, find the probability it was made by Chrysler.

(a) About 0.274 ; (b) About 0.332 ; (c) About 0.418 ; (d) About 0.232 ; (e) About 0.376 ;

Use Statkey for the following numbers:

18 54 64 46 91 38 25 45 67 57 48 44 63

83 84 79 52 54 41 52 56 76 41 75 79 68

28 55 77 68 33 65 59 37 61 70 47 51 32

56 19 45 29 63 75 39 84 48 42 36

1. Does this data come from a "mound-shaped", distribution? Justify your answer.

2. Is the data symmetric or skewed? Justify your answer.

3. Are there any TRUE outliers, what are they, and what percent of the sample are they? Justify your answer.

4. Bell-shaped (normal) sample? why?

On April 1, 1992, New Jersey’s minimum wage was increased from $4.25 to $5.05 per hour, while the minimum wage in Pennsylvania stayed at $4.25 per hour. Energetic students collected data on 410 fast food restaurants in New Jersey (the treatment group) and eastern Pennsylvania (the control group). The “before” period is February 1992, and the “after” period is November 1992. Using these data, we will estimate the effect of the “treatment,” raising the New Jersey minimum wage on employment at fast food restaurants in New Jersey (i.e., H_0:δ=0 versus H_A:δ<0). It is easier and more general to use the regression format to compute the differences-in-differences estimate using sample means. Let y=FTE employment , the treatment variable is the indicator variable NJ=1 if observation is from New Jersey, and zero if from Pennsylvania. The time indicator is D=1 if the observation is from November and zero if it is from February. (a.)Write out the regression equation. (b)Report the least squares estimates . (c)At the α=.05 level of significance the regression region for the left tail test in above hypotheses is t≤-1.645, what is your conclusion? (d)As with randomized control (quasi) experiments it is interesting to see the robustness of the result from (c). Please, add indicator variables for fast food chain and whether the restaurant was company-owned rather than franchise-owned. These changes alter the DID estimator? (e)Please, add indicator variables for geographical regions within the survey area. These changes alter the DID estimator?

Case 1 Instruction (Accounting Application) Use the MS Excel tabular graphical methods of descriptive statistics to summarize the sample data in the data set named PelicanStores in Case 1 folder. The managerial report should contain summaries such as:

1. A frequency and relative frequency distributions for the methods of payment (different cards). (20%)

2. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from regular customers. (20%)

3. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from married female. (20%)

4. Apply the location method to calculate the 60th percentile manually of net sales for each method (card) of payment. Please indicate which card has the highest 60th percentile and show the process. (20%)

5. Apply Chebyshev’s Theorem to calculate the range (i.e. $ to $) of at least 75% of the net sales must fall within for the Proprietary Card payment. (20%) (Hint: What is the z-score for at least 75% of data range?)

An economist wonders if corporate productivity in some countries is more volatile than in other countries. One measure of a company's productivity is annual percentage yield based on total company assets.

A random sample of leading companies in France gave the following percentage yields based on assets.

Use a calculator to verify that the sample variance is s² ≈ 2.046 for this sample of French companies.

Another random sample of leading companies in Germany gave the following percentage yields based on assets.

Use a calculator to verify that s² ≈ 1.044 for this sample of German companies.

Test the claim that there is a difference (either way) in the population variance of percentage yields for leading companies in France and Germany. Use a 5% level of significance. How could your test conclusion relate to the economist's question regarding volatility (data spread) of corporate productivity of large companies in France compared with companies in Germany? (a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²     H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population.     The populations follow independent normal distributions. The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.200 0.100 < p-value < 0.200     0.050 < p-value < 0.100 0.020 < p-value < 0.050 0.002 < p-value < 0.020 p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the French companies. Reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the French companies.     Reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is different in both companies. Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is different in both companies.

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 158 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month?

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Fatal Accidents 17 10 12 19 9 10 10 12 12 18 17 12

Step 1 of 10: State the null and alternative hypothesis. Step 2 of 10: What does the null hypothesis indicate about the proportions of fatal accidents during each month? Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category. Step 4 of 10: Find the expected value for the number of fatal accidents that occurred in January. Round your answer to two decimal places. Step 5 of 10: Find the expected value for the number of fatal accidents that occurred in April. Round your answer to two decimal places. Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places. Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem. Step 8 of 10: Find the critical value of the test at the 0.1 level of significance. Round your answer to three decimal places. Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.1 level of significance. Step 10 of 10: State the conclusion of the hypothesis test at the 0.1 level of significance.