Test whether there is a difference between two groups.

45 out of 71 in group 1

56 of 99 Group 2

p̂1 =

p̂2 =

p̂ =

Test Statistic =

p-value =

There are 10 CS students, 12 CPRE students and 8 SE students, to form a committee.

(a) How many different committees of size 3 can you pick if you need one representative from each program?

(b) How many different committees of size 2 can you pick if you cannot pick both representatives from the same program?

(c) In how many ways can you pick a president, a secretary, and a treasurer from the group of students if they cannot all be CS students?

1. Are professional jobs held in the computing industry independent of the number of years a person has worked in the industry? Suppose 246 workers are interviewed. Use the results to obtained to determine whether type of professional job held in the computer industry is independent of years worked in the industry. Take a = 0.0

Professional position

1. A corporation owns several companies. The strategic planner for the corporation believes amount spent on advertising can to some extent be a predictor of total sales. As an aid in long term planning, she gathers the following sales and advertising information from several of the companies in millions for the year 2019.

1. Develop the equation of the simple regression line to predict sales on advertising expenditures using these data.                                                                                                              [10 Marks]
2. Find out the sales that are likely to be attained when advertising expenditure is 25

million.                                                                                                           [2 Marks]

3. Compute the coefficient of correlation and coefficient of determination and interpret their values. [4 Marks]
4. Test the hypothesis that the population correlation coefficient is zero at 5% level of significance. [4 Marks]

A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below.

Company   Compensation   Return
A   14.98   74.48
B   4.61   63.62
C   6.15   148.21
D   1.11   30.35
E   1.54   11.94
F   3.28   29.09
G   11.06   0.64
H   7.77   64.16
I   8.23   50.41
J   4.47   53.19
K   21.39   21.94
L   5.23   33.68

​(a) Draw a scatter diagram of the​ data, treating age as the explanatory variable. What type of​ relation, if​ any, appears to exist between age and HDL​ cholesterol?

C. There does not appear to be a relation. - Correct Answer

​(b) Determine the​ least-squares regression equation from the sample data.

ŷ=-0.129x+50.936

​ (Round to three decimal places as​ needed.)

​(c) Are there any outliers or influential​ observations?

No Your answer is correct

(d) Assuming the residuals are normally​ distributed, test whether a linear relation exists between age and HDL cholesterol levels at the α=0.01level of significance. What are the null and alternative​ hypotheses?

C. H0​: β1=​0; H1​: β1≠0 - Correct Answer

Use technology to compute the​ P-value.

The​ P-value is 0.546

​(Round to three decimal places as​ needed.)

What conclusion can be drawn at α=0.01 level of​ significance?

A. Do not reject the null hypothesis because the​ P-value is greater than α=0.01. ​

(e) Assuming the residuals are normally​ distributed, construct a​ 95% confidence interval about the slope of the true​ least-squares regression line.

Lower Bound -0.217

(Round to three decimal places as​ needed.)

Upper Bound - __?___

(Round to three decimal places as​ needed.)

The daily exchange rate for currencies fluctuates on a daily basis due to many economic conditions affecting the business cycle. The exchange rate for a twelve month period in the year 2004 between the US dollar and the EURO shows an approximately normally distributed behavior with a mean exchange rate of 0.804 euros for every dollar and a standard deviation of 0.0255.

Find the following:

A) The probability that the exchange rate between the pair of currencies between 0.798 and 0.8100.

B) The probability that the exchange rate will be larger than 0.845 euros for every dollar.

C) The exchange rate such that 98% of the data falls below it.

D) If the standard deviation is changed from the stated value to 0.03, what will the answers in (A) through (C) be.

A common criticism of surveys is that they poll only a very small percentage of the population and therefore cannot be accurate. Is a sample of only 1961 adults taken from a population of 225,139,000 adults a sample size that is too small? Show why the sample size of 1961 is or is not too small.

1. The following set of data represents the distribution of annual salaries of a random sample of

100managers in a large multinational company:

1. Calculate the mean and standard deviation. [5 Marks]
2. The company chairman claims that the managers in the company earn on average annual salary in excess of £ 35,500. Use the result in (i) to test the chairman’s claim at 5% level of significance. [5 Marks]

sample size is 105. thanks

We have a one parameter statistical model.

Probability model: {f(x;θ)=x/(2θ^2), θ>0 and x is an element of (0, θ].

Sampling model: X=(X₁,...X_n) is random.

By stating likelihood and log likelihood functions, calculate the maximum likelihood estimator of θ. Differentiation can't be used to solve this problem.

13) A study published in 2008 in the American Journal of Health Promotion (Volume 22, Issue 6) by researchers at the University of Minnesota (U of M) found that 124 out of 1,923 U of M females had over $6,000 in credit card debt while 61 out of 1,236 males had over $6,000 in credit card debt.

a) Verify that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in two proportions.

b) Construct a 95% confidence interval for the difference between the proportions of female and male University of Minnesota students who have more than $6,000 in credit card debt (pf - pm).

d) Does the interval contain the difference in sample proportions of female and male University of Minnesota students who have more than $6000 in credit card debt Phat_f - Phat_m ?

e) Explain why the previous question is silly and did not require you to even look at the interval.

f) According to your interval in (b) is it reasonable to assume that there is no difference between men and women at U of M regarding credit card debt? Clearly answer “yes” or “no.” ______ The briefly explain your answer? [3pt]

Sulfur compounds cause “off-odors”in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human
nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (μg/l). The untrained noses
of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students:

31 31 43 36 23 34 32 30 20 24

(a) Assume that the standard deviation of the odor threshold for untrained noses is known to be σ = 7 μg/l. Briefly discuss the other two “simple conditions,”
using a stemplot to verify that the distribution is roughly symmetric with no outliers.

(b) Give a 95% confidence interval for the mean DMS odor threshold among all students.

It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.25 5.75 6.25 6.75 7.75 y 11 18 28 36 49

Find x

It the​ 1980s, it was generally believed that congenital abnormalities affected about 7​% of a large​ nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 409 randomly selected children and found that 58 of them showed signs of an abnormality. Is this strong evidence that the risk has​ increased? (We consider a​ P-value of around 5% to represent reasonable​ evidence.) Complete parts a through f. Assume the independence assumption is met.

​a) Write appropriate hypotheses. Let p be the proportion of children with genetic abnormalities. Choose the correct answer below.

A.H0​: p=0.1418 vs. HA​: p>0.1418   B.H0​:p=0.1418 vs. HA​: p≠0.1418

C.H0​: p=0.1418 vs. HA​: p<0.1418 D.H0​:p=0.07 vs. HA​: p>0.07

E.H0​: p=0.07 vs. HA​: p<0.07   F. H0​: p=0.07 vs. HA​: p≠0.07

b) Check the necessary assumptions. Which of the following are​ satisfied? Select all that apply.

A.Less than​ 10% of the population was sampled.

B.There are more than 10 successes and 10 failures.

C.The independence assumption is satisfied.

D.The sample is random.

c) Perform the mechanics of the test. What is the​ P-value?

​P-value=

​d) Explain carefully what the​ P-value means in this context. Choose the correct answer below.

A.The​ P-value is the chance of observing 58 or more children with genetic abnormalities in a random sample of 409 children.

B.The​ P-value is the chance of observing 7​% of children with genetic abnormalities.

C.The​ P-value is the actual percentage of children who have genetic abnormalities.

D.The​ P-value is the chance of observing 58 or more children with genetic abnormalities in a random sample of 409 children if 7​%of children actually have genetic abnormalities.

​e) What's your​ conclusion?

A.Reject H0.There is sufficient evidence that more than 7​% of the​ nation's children have genetic abnormalities.

B.Fail to rejectFail to reject H0.There is sufficient evidence that more than 7​% of the​ nation's children have genetic abnormalities.

C.Fail to rejectFail to reject H0.There is not is not sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

D.Reject H0.There is not is not sufficient evidence that more than 7​% of the​ nation's children have genetic abnormalities.

​f) Do environmental chemicals cause congenital​ abnormalities?

A.​Yes, the conclusion of the hypothesis test shows that environmental chemicals cause genetic abnormalities.

B.It is unknown if environmental chemicals cause genetic​ abnormalities, because the hypothesis test does not indicate the cause of any changes.

C.​No, the conclusion of the hypothesis test shows that environmental chemicals do not cause genetic abnormalities.

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 259.5 and a standard deviation of 66.4. ​(All units are 1000 ​cells/mu​L.) Using the empirical​ rule, find each approximate percentage below.

a.

What is the approximate percentage of women with platelet counts within 3 standard deviations of the​ mean, or between 60.3 and 458.7​?

b.

What is the approximate percentage of women with platelet counts between 126.7 and 392.3​?