Random samples of size n = 60 were selected from a binomial population with p = 0.2. Use the normal distribution to approximate the following probabilities. (Round your answers to four decimal places.)

(a)    

P(p̂ ≤ 0.22) =

(b)    

P(0.18 ≤ p̂ ≤ 0.22) =

Consider the following measurements of blood hemoglobin concentrations (in g/dL) from three human populations at different geographic locations:

population1 = [ 14.7 , 15.22, 15.28, 16.58, 15.10 ]

population2 = [ 15.66, 15.91, 14.41, 14.73, 15.09]

population3 = [ 17.12, 16.42, 16.43, 17.33]

Perform ANOVA to check if any of these populations have different mean hemoglobin concentrations. (Assume that all the ANOVA requirements such as normality, equal variances and random samples are met.) After you perform ANOVA perform a Tukey-Kramer post-hoc test at a significance level of 0.05 to see which populations actually have different means. As usual, round all answers to two digits after the decimal point. (Make sure you round off to at least three digits any intermediate results in order to obtain the required precision of the final answers.) For any questions, which ask about differences in means or test statistics, which depend on differences in means provide absolute values. In other words if you get a negative value, multiply by -1 to make it positive.

QUESTION 13

1. What is the standard error of the difference between the means of population 2 and population 3, needed to calculate the Tukey-Kramer q-statistic?  

QUESTION 14

1. What is the Tukey-Kramer q-statistic for populations 2 and 3? (Report the absolute value, if you get a negative number, multiply by -1)

QUESTION 15

1. For the hemoglobin data of the three populations, what is the critical value of the q-statistic required to reject the null hypothesis of the Tukey-Kramer test at a significance level of 0.05?

QUESTION 16

1. Which populations are have different means according to the results of the Tukey-Kramer test? Select all that apply, you may need to select more than one correct answer to get credit for this question.

   		Population 1 and Population 2
   		Population 1 and Population 3
   		Population 2 and Population 3
   		None of the above. All populations have the same means.

A car company claims that their Super Spiffy Sedan averages 31 mpg. You randomly select 8 Super Spiffies from local car dealerships and test their gas mileage under similar conditions.

You get the following MPG scores:

We wan to test whether the actual gas mileage for these cars deviate significantly from 31 (alpha = .05).

1- Are we given the value of the population mean (μ)?

2- What is the the standard error?

3- What is the the null hypothesis?

4- What is the the value of the test statistic?

5- Based on the p-value you obtained, should we reject the null hypothesis at significance level α = 0.05?

6- What is a 95% confidence interval for the mean actual gas mileage of the company's cars?

Suppose you work at a local state hospital. In 2015, the infectious disease department of the hospital was operating at max capacity. Your supervisor has given you the job of presenting to the hospital leadership board about the number of patients who contracted infections while at 30 different hospitals in your state in 2015. The board will use your findings to make informed decisions about possible expansion of the infectious disease department. You will review the data, create visuals for the data, and create a presentation for the hospital leadership board to help with the decision.

2015
Hospital   Infections *Secondary column are the # of infections*
1 89
2 58
3 96
4 206
5 31
6 16
7 249
8 79
9 29
10 6
11 222
12 108
13 58
14 54
15 81
16 64
17 9
18 130
19 37
20 121
21 27
22 6
23 95
24 7
25 18
26 37
27 140
28 74
29 134
30 184

   Infections
Min=
Q1=   
Median=   
Q3=   
Max=   

Check for Outliers  
IQR=   
Lower=   
Upper=   

Infection Class Frequency
6 - 81=   
82 - 156=
157-231=   
232-306=   

•   Use the following data to complete the values, a histogram, box & whisker plot, bell curve with distribution, and answer the following questions below.
•   How did the outliers impact the mean and median? How did they impact the histogram?
•   How would you describe the shape of your histogram? Is it skewed?
•   Which do you think is a better measure of central tendency, median or mean? Why?
•   How would you describe how spread out your data is? What did you calculate or which visual supports your conclusion on how spread out the data is?
•   How does your data support your conclusion?

The Pew Research Center Internet Project conducted a survey of 857 Internet users. This survey provided a variety of statistics on them. If required, round your answers to four decimal places.

(a) The sample survey showed that 90% of respondents said the Internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. 0.880 to 0.920

(b) The sample survey showed that 67% of Internet users said the Internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends. to

(c) Fifty-six percent of Internet users have seen an online group come together to help a person or community solve a problem, whereas only 25% have left an online group because of unpleasant interaction. Develop a 95% confidence interval for the proportion of Internet users who say online groups have helped solve a problem. to

(d) Compare the margin of error for the interval estimates in parts (a), (b), and (c). How is the margin of error related to the sample proportion? The margin of error as p gets closer to .50.

1) You conduct a stepwise regression according to the following procedure:

Step 1:        HS_SCI only

Step 2:        HS_SCI and HS_ENG

Step 3:        HS_SCI, HS_ENG and HS_MATH

Step 4:        HS_SCI, HS_ENG, HS_MATH and PARENT EDUC

Step 5:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC AND GENDER

Step 6:        HS_SCI, HS_ENG and HS_MATH, PARENT EDUC, GENDER and ATAR

Present the regression output for each of the six steps.

Choice of reference category: It is recommended that you choose U (undergraduate education) as the reference category for the categorical variable: PARENT EDUC.                                                   

2) For eachof the independent variables contained in the regression model in Step 5, fullyinterpret the regression (slope) coefficients and comment on their statistical significance.

In discussing statistical significance of a regression coefficient, you have to justify your choice of a one or two tail test.

3) In stepwise regression Step 6you noticed that the regression coefficient of ATAR is negative (!). Does this result surprise you, given the correlation of ATAR and GPA? Why/Why not? Does the inclusion of ATAR improve overall model fit? Discuss fully.   

DATA SAET:

It has been suggested that pets provide a supportive social function in buffering adverse response to physiological stressors. A sample of 20 pet owners were subjected to stressors with their pets present and their heart rates were measured (mean=75.32 beats per minute). A previous study found that heart rates of individuals under stress in this population is normally distributed with mean = 82.18 and sigma = 8.15.

A. Construct a 90% confidence interval for μ.

Interpret the 90% confidence interval above:

B. Conduct a 2-sided test to see if the presence of pets was associated with reduced stress. Show all hypothesis testing steps.

i. Hypothesis statements

ii. Test statistic

iii. p-value =

iv. Conclusion of significance

Consider the following measurements of blood hemoglobin concentrations (in g/dL) from three human populations at different geographic locations:

population1 = [ 14.7 , 15.22, 15.28, 16.58, 15.10 ]

population2 = [ 15.66, 15.91, 14.41, 14.73, 15.09]

population3 = [ 17.12, 16.42, 16.43, 17.33]

Perform ANOVA to check if any of these populations have different mean hemoglobin concentrations. (Assume that all the ANOVA requirements such as normality, equal variances and random samples are met.) After you perform ANOVA perform a Tukey-Kramer post-hoc test at a significance level of 0.05 to see which populations actually have different means. As usual, round all answers to two digits after the decimal point. (Make sure you round off to at least three digits any intermediate results in order to obtain the required precision of the final answers.) For any questions, which ask about differences in means or test statistics, which depend on differences in means provide absolute values. In other words if you get a negative value, multiply by -1 to make it positive.

QUESTION 9

1. What is the standard error of the difference between the means of population 1 and population 2, needed to calculate the Tukey-Kramer q-statistic?

QUESTION 10

1. What is the Tukey-Kramer q-statistic for populations 1 and 2? (Report the absolute value, if you get a negative number, multiply by -1)

QUESTION 11

1. What is the standard error of the difference between the means of population 1 and population 3, needed to calculate the Tukey-Kramer q-statistic?

QUESTION 12

1. What is the Tukey-Kramer q-statistic for populations 1 and 3? (Report the absolute value, if you get a negative number, multiply by -1)

A manufacturing process produces semiconductor chips with a known failure rate of 6.3%. Assume that the chip failures are independent of one another. You will be producing 2,000 chips tomorrow.

e. Find the probability that you will produce more than 120 defects.

f. You just learned that you will need to ship 1,860 working chips out of tomorrow’s production of 2,000. What are the chances that you will succeed? Will you need to increase the scheduled number produced?

g. If you schedule 2,100 chips for production, what is the probability that you will be able to ship 1,860 working ones?

Consider the following measurements of blood hemoglobin concentrations (in g/dL) from three human populations at different geographic locations:

population1 = [ 14.7 , 15.22, 15.28, 16.58, 15.10 ]

population2 = [ 15.66, 15.91, 14.41, 14.73, 15.09]

population3 = [ 17.12, 16.42, 16.43, 17.33]

Perform ANOVA to check if any of these populations have different mean hemoglobin concentrations. (Assume that all the ANOVA requirements such as normality, equal variances and random samples are met.) After you perform ANOVA perform a Tukey-Kramer post-hoc test at a significance level of 0.05 to see which populations actually have different means. As usual, round all answers to two digits after the decimal point. (Make sure you round off to at least three digits any intermediate results in order to obtain the required precision of the final answers.) For any questions, which ask about differences in means or test statistics, which depend on differences in means provide absolute values. In other words if you get a negative value, multiply by -1 to make it positive.

QUESTION 1

1. For the three populations, what is the value of SSgroups in the ANOVA table?

QUESTION 2

1. For the three populations, what is the value of SSerror in the ANOVA table?

QUESTION 3

1. For the three populations, how many degrees of freedom are there for the groups?  

QUESTION 4

1. For the three populations, how many degrees of freedom are there for the error?

8) (1 point) Melanism in Moths. Melanism is the process by which animals produce melanin to darken body tissues and produce color variation. Researchers at Oxford University suspected increased levels of pollution in London may be influencing the evolution of Lepidoptera, a species of moth native to the area that took on one of two distinct camouflage schemes: "light" and "dark." They surveyed a sample of dark and light moths on birch trees and labelled each "conspicuous" if it was visible from 30 yards away or "inconspicuous" if it was not. The table below shows the number of moths of each color that were conspicuous and inconspicuous. Use this data to investigate the researchers' theory that increased levels of pollution might provide an advantage to "dark" moths over "light" ones.

Conduct a test for the stated null and alternative hypotheses. Use αα = and round numeric answers to four decimal places.

H0H0: The variables use of color and detectability are independent.

HAHA: The variables use of color and detectability are not independent.

1. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

2. Calculate the degrees of freedom for this hypothesis test.

3. Report the p-value for this hypothesis test out to four decimal places.

p-value =

4. Based on the p-value, we have:
A. strong evidence
B. extremely strong evidence
C. little evidence
D. some evidence
E. very strong evidence
F. Reject H0H0
that the null model is not a good fit for our observed data.

8) (1 point) A researcher is interested in whether the number of years of formal education is related to a person's decision to never smoke, continue to smoke, or quit smoking cigarettes. The data below represent the smoking status by level of education for residents of the United States 18 years or older from a random sample of 200 residents. Round all numeric answers to four decimal places.

1. Select the name of the test that should be used to assess the hypotheses:

H0H0: "Smoking Status" is independent of "Education Level"

HAHA: "Smoking Status" is not independent of "Education Level"

A. X2X2 goodness of fit
B. X2X2 test of a single variance
C. X2X2 test of independence

2. Under the null hypothesis, what is the expected number for people with an education of Less than high school and a smoking status of Former?

3. Calculate the X2X2 test statistic.

4.What was the contribution of Former smokers who attended Less than high school toward this test statistic?

5. What are the degrees of freedom for this test?

6. What is the p-value for this test?

7. Based on the p-value, we have:
A. some evidence
B. strong evidence
C. little evidence
D. extremely strong evidence
E. very strong evidence
that the null model is not a good fit for our observed data.

8. Which of the following is a necessary condition in order for the hypothesis test results to be valid? Check all that apply.

A. There must be an observed count of at least 5 in every cell of the table.
B. The population data must be normally distributed.
C. The observations must be independent of one another.
D. There must be at least 10 "yes" and 10 "no" observations for each variable.
E. There must be an expected count of at least 5 in every cell of the table.

7) (1 point) A package delivery service wants to compare the proportion of on-time deliveries for two of its major service areas. In City A, 251 out of a random sample of 310 deliveries were on time. A random sample of 324 deliveries in City B showed that 243 were on time.

1. Calculate the difference in the sample proportion for the delivery times in the two cities.

p^CityA−p^CityBp^CityA−p^CityB =

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of deliveries that are on time in City A is different from than the proportion in City B?

A. H0:pA=pBH0:pA=pB, HA:pA<pBHA:pA<pB
B. H0:pA=pBH0:pA=pB, HA:pA≠pBHA:pA≠pB
C. H0:pA=pBH0:pA=pB, HA:pA>pBHA:pA>pB

3. Calculate the pooled estimate of the sample proportion.

p^p^ =

4. Is the success-failure condition met for this scenario?

A. No
B. Yes

5. Calculate the test statistic for this hypothesis test.

? z t X^2 F  =

6. Calculate the p-value for this hypothesis test.

p-value =

7. Based on the p-value, we have:
A. some evidence
B. very strong evidence
C. extremely strong evidence
D. strong evidence
E. little evidence
that the null model is not a good fit for our observed data.

8. Compute a 90% confidence interval for the difference p^CityA−p^CityBp^CityA−p^CityB.

( , )

7) (1 point) A Washington Post article from 2009 reported that "support for a government-run health-care plan to compete with private insurers has rebounded from its summertime lows and wins clear majority support from the public." More specifically, 67 percent of Democrats back the plan, while almost nine in 10 Republicans oppose it. Independents divide 54 percent in favor of and 42 percent against the legislation. 4% responded with "other". There were 815 Democrats, 566 Republicans and 780 Independents surveyed. Round all results to 4 decimal places.

a. Calculate a 95% confidence interval for the difference between pDemocrat−pIndependentpDemocrat−pIndependent . We have already checked conditions for you.

Lower:

Upper:

b. True or false: If we had picked a random Democrat and a random Independent at the time of this poll, it is more likely that the Democrat would support the public option than the Independent.  ? True False

1. Calculate Pearson’s r correlation coefficient?

2. What does the result you obtain say? (10points)

Now calculate whether the result obtained is statistically significant

3. State the Null and Alternative hypotheses? (5 points)

4. Establish your decision criteria and determine t critical (df = N-2).

5. Determine t calculated?

6. Are the results significant at the 5% level and explain what it means in terms of the Null hypothesis? (20 points)