A simple random sample of 70 customers is taken froma customer information file and the average age is 36. The population standard deviation o is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4.5. 2. Test the hypothesis that the population mean age is greater than 33 using the critical value approach and a 0.05 level of significance. а. Test the hypothesis that the population mean age is less than 38 using the p- value approach and a 0.05 level of significance. b. Test the hypothesis that the population mean age is different from 32 using the p-value approach and a 0.05 level of significance. с.

The chartered financial analyst (CFA) is a designation earned after taking three annual exams (CFA I,II, and III). The exams are taken in early June. Candidates who pass an exam are eligible to take the exam for the next level in the following year. The pass rates for levels I, II, and III are 0.58, 0.75, and 0.81, respectively. Suppose that 3,000 candidates take the level I exam, 2,500 take the level II exam and 2,000 take the level III exam. A randomly selected candidate who took a CFA exam tells you that he has passed the exam. What is the probability that he took the CFA I exam? Probability =

In your own words write a summary about anti smoking messages in the United state

1. We are conducting a one-way between groups ANOVA. We have 50 people in each condition. Each person rates how much they like their assigned food (pizza, burger, or taco) on a scale of 1 to 5 (1 = hate this food, 5 = favorite food ever). We run a hypothesis test and find a significant statistic. What does this mean?

1. Calculate all the appropriate HSDs for the following groups:

Pizza Mean: 2.3; Burger Mean: 4.5; Taco Mean: 3.7; Standard Error (s_M): .32

2. If the critical value found in the q table is -6.236, are any comparisons significant? What do your findings mean?

The following table shows the unemployment rate for people with various education levels in the United States. Suppose we are interested in predicting the unemployment rate based on the education level.

Give the equation of the regression line. (2pts)

Write a sentence interpreting the y-intercept. (2pts)

Write a sentence interpreting the slope. (2pts)

Predict the unemployment rate for the group of people who have 10 years of education. (2pts)

Compute the residual for the group of people who have completed 12 years of education. (2pts)

Compute the residual for the group of people who have completed 5 years of education. (2pts)

Compute the residual for the group of people who have completed 16 years of education. (2pts)

A species of marine arthropod lives in seawater that contains calcium in a concentration of 32 mmole/kg of sea water. Thirteen of the animals are collected and the calcium concentration in coelomic fluid are determined. Results are summarized in the table below. A researcher plans to use these data to test H0: (mu) = 32 versus HA: (mu) (DNE) 32 at a significance level of 0.05, where (mu) = the mean calcium concentration in this arthropod’s coelomic fluid.

4. Compute the power of the test when (mu) = 31.5.
5. Determine the sample size necessary in order to achieve a power of 80% when (mu) = 31.5.

Let X and Y be two independent random variables. Assume that X is Negative-
Binomial(2, θ) and Y is Negative-Binomial(3, θ) distributed. Let Z be another random

variable, Z = X + Y .
(a) Find the following probabilities: P(Z = 0), P(Z = 1) and P(Z = 2);
(b) Can you guess what is the distribution of Z?

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?