# A researcher in the West Coast of the U.S. wants to estimate the amount of a newly discovered antibody in human blood

Dated: 1st Jul'15 09:45 AM
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1. A researcher in the West Coast of the U.S. wants to estimate the amount of a newly discovered antibody in human blood. His research funds will only let him obtain blood samples from 41 people, so he decides to construct a two-sided 90% confidence interval thinking it will give him a more precise estimate of the mean antibody level in the population. Another researcher on the East Coast of the United States is researching the same antibody, but has more research funding and can afford to obtain blood samples from 121 people. The East Coast researcher decides to construct a two-sided 99% confidence interval. Which researcher will have the more precise estimate? State your reason for choosing your answer. It may help to imagine that the sample standard deviation will be about the same for both samples.

2. Identify a pair of variables for which you would expect to see a strong correlation but not a cause-and-effect relationship. Suggest an explanation for the association.

3. Twenty years ago, postal employees worked for the postal service an average of 7.5 years. Recently, a sample of 100 postal employees revealed that the average time these employees had worked for the postal service was () = 7 years. The population of employee lengths of service has a standard deviation = 5 years. Has decreased from the mean of 7.5 years of 20 years ago? Conduct a hypothesis test (use H0: µ = 7.5). Use a .05 significance level. Is this evidence that the average length of employment with the postal service has decreased from twenty years ago?

4. The salaries of the CEOs and the stock prices of 24 companies are shown in this scatterplot. A CEO uses this relation to argue there is a positive correlation between CEO salary and the Stock Price, and therefore, for the good sake of the company's stock value, his salary should be increased. Do you agree with his argument? Explain why or why not.

Dr. Hanson's mother Sally and her sister Pat have a rivalry about who makes the better apple pie. Sally makes two pies and has 16 people selected at random from her church eat a piece of pie and rate her pies on a scale of 1-10. The 16 ratings are as follows: 6, 8, 3, 9, 9, 9, 8, 8, 6, 7, 8, 7, 6, 7, 6, 8. Her sister Pat had 15 randomly selected people try a piece of pie at her church and the ratings were:7, 3, 9, 9, 8, 6, 6, 6, 7, 4, 8, 6, 10, 2, 7.

5. Use the SPSS output to determine if there is sufficient evidence to conclude that Sally bakes a better pie than Pat (i.e., the average rating for Sally at her church is higher than the average rating for Pat at her church). Justify your conclusion.

6. A nutritionist thinks the average person with an income below the poverty level gets less than the recommended daily allowance (RDA) of 800 mg of calcium. To test her conjecture, she obtains the daily intakes of calcium for a random sample of 45 people with incomes below the poverty level. The mean of the sample is 737.3 mg with sample standard deviation of 262.2 mg. Is there sufficient evidence at the alpha =0.05 level to support the researcher's claim?

7. Shown below are the results of a one sample t test. Make up a problem that someone could solve using the printout. Do not make up the data. Just assume the data were collected and produced the given statistics.

8. Suppose you want to determine whether students' expected grades at the beginning of an introduction to statistics course are positively related to their final course grade. Write the null and alternative hypotheses in words.

Ten states were randomly selected from among the 50 United States. This data set presents the percentage of households in each state that were below the poverty level (Poverty Rate) and the percentage of adults in the state who had earned a high school degree or higher (HS and Above). In the table is the mean and standard deviation for each variable, and the correlation for the two variables. You do not need to calculate these values.

9. One of the points is suspected of being a bivariate outlier. When this point is removed, the new correlation is r = -.833. Is this point likely to be a bivariate outlier? Explain your answer.

The following stemplot represents the yearly percentage increases in Dickinson's comprehensive fees over the past 22 years. (3 | 8 means that one year had a percentage increase of 3.8%.)

10. The median percentage increase is 7.75%. Without calculating the mean, do you expect it to be greater than the median or less than the median. Why?

The following summaries and boxplots represent 40 daily closing prices for three different stocks, A, B and C.

11. What shape histograms would you expect to see for each of the stocks, based on their boxplots? Sketch possible histograms for Stock A, Stock B, and Stock C.

We want to know if reading achievement differs for children who have been taught using the following four approaches: Phonics, Whole Word, RP1, and Literacy4All.

12. Set up and fill in the ANOVA summary table. Do this very carefully.

Items 13 and 14 refer to the following situation:

A panel of trained testers judged the flavor quality of different vanilla frozen desserts (frozen yogurts, ice milks, other frozen desserts) measured on a scale from 0 to 100. The data are from a Consumer Reports article "Low-fat frozen desserts: Better for you than ice cream?" (August, 1992). Here is a graphical summary of the data.

13. Explain briefly why ANOVA was the appropriate analysis for these data.

14. Finish the ANOVA table giving the F-statistic, degrees of freedom, and approximating the p-value. Show your work. What is your conclusion about the flavor quality of the different desserts?

For each research situation below (Q15 – Q21), decide what statistical procedure would most likely be used to answer the research question posed. Assume all assumptions have been met for using the procedure.

15. Do college grade point averages differ for male athletes in major sports (e.g., football), minor sports (e.g., swimming), and intramural sports?

a. Test the difference between two means (independent samples).

b. Test one mean against a hypothesized constant.

c. Test the difference in means between two paired or dependent samples.

d. Test for a difference in more than two means (one way ANOVA).

e. Test that a correlation coefficient is not equal to 0 correlation analysis.

f. Use a chi-squared test of association.

g. Construct Confidence Interval(s).

16. Does knowing high school seniors' IQ scores indicate anything about their high school graduation grade point averages?

a. Test one mean against a hypothesized constant.

b. Test the difference between two means (independent samples).

c. Test that a correlation coefficient is not equal to 0 correlation analysis.

d. Test for a difference in more than two means (one way ANOVA).

e. Test the difference in means between two paired or dependent samples.

f. Use a chi-squared test of association.

g. Construct Confidence Interval(s).

17. Is there a relationship between a person's sociability and cheerfulness? (Assume sociability and cheerfulness can be measured by valid and reliable instruments.)

a. Test one mean against a hypothesized constant.

b. Test the difference between two means (independent samples).

c. Test the difference in means between two paired or dependent samples.

d. Test for a difference in more than two means (one way ANOVA).

e. Test that a correlation coefficient is not equal to 0 correlation analysis.

f. Use a chi-squared test of association.

g. Construct Confidence Interval(s).

18. We have the geography test scores from a random sample of 100 fifth grade students. What are the most plausible values for the mean geography score for all fifth graders?

a. Calculate the appropriate confidence interval.

b. Use the normal curve.

c. H0:= k

d. H0:1 =2 (independent samples)

e. H0:1 =2 (dependent samples)

19. Is there a difference in average math performance between eighth grade female and male students?

a. Calculate the appropriate confidence interval.

b. Use the normal curve.

c. H0:= k

d. H0:1 =2 (independent samples)

e. H0:1 =2 (dependent samples)

20. Do high school boys who have been arrested once score above the average U.S. high school boy on a standardized scale of aggressiveness?

a. Calculate the appropriate confidence interval.

b. Use the normal curve.

c. H0:= k

d. H0:1 =2 (independent samples)

e. H0:1 =2 (dependent samples)

21. For our research study, we need to select computer programmers who are in the lowest 25% of the U.S. population in sociability. What is the cut-off on a standardized questionnaire of sociability ratings?

a. Calculate the appropriate confidence interval.

b. Use the normal curve.

c. H0:= k

d. H0:1 =2 (independent samples)

e. H0:1 =2 (dependent samples)

22. Which of the following values is most likely to represent the correlation coefficient for the data shown in this scatterplot?

a. r = -0.67

b. r = -0.10

c. r = 0.71

d. r = 0.93

e. r = 0.96

f. r = 1.00

23. Which of the following values is most likely to represent the correlation coefficient for the data shown in this scatterplot?

a. r = -0.67

b. r = -0.10

c. r = 0.71

d. r = 0.93

e. r = 0.96

f. r = 1.00

24. Which of the following values is most likely to represent the correlation coefficient for the data shown in this scatterplot?

a. r = -0.67

b. r = -0.10

c. r = 0.71

d. r = 0.93

e. r = 0.96

f. r = 1.00

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Solution- A researcher in the West Coast of the U.S. wants to estimate the amount of a newly discovered antibody
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