A) In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

B)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Do professional golfers play better in their last round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first and last rounds in the tournament.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

A study was conducted to investigate the relationship between maternal smoking during pregnancy and the presence of congenital malformations in the child. Among children who suffer from an abnormality other than Down’s syndrome or an oral cleft, 32.8% have mothers who smoked during pregnancy. You wish to determine if this proportion is the same for those children born with an oral cleft. In a random sample of 27 infants with an oral cleft, 15 had mothers who smoked during pregnancy.

a. What is the estimate of the proportion of infants born with oral clefts whose mothers smoked during pregnancy?

b. Construct a 95% confidence interval for the true population proportion.

c. What are the Null and Alternative Hypotheses of this test?

d. Conduct the test at the 0.05 level of significance.

e. Using Stata, determine the sample size required to have 80% power to detect an alternative of 40% at the 0.01 level of significance.

The following partial ANOVA table was based on an experiment performed as a two-factor design with 2 levels of factor A, 3 levels of factor B, and 5 observations on each treatment. It was determined that treatment groups were independently selected from a normal distribution with the same variance for each treatment.

a) Fill in the missing entries in the ANOVA table.

b) Test the hypothesis of no interaction between the factors at a 5% level of significance. Your answer should show assumptions, hypotheses, and conclusions.

c) Indicate whether testing for the main effects is appropriate, and if so show, the results of the tests; if not, indicate why testing for the main effects is not justified. Your answer should show assumptions, hypotheses, and conclusions.

A questionnaire collects information from UTS students on gender and whether or not the student smokes. The resultant two-way table is shown below.

Women Men Total

Don’t smoke 153 166 319

Smoke 16 27 43

Total 169 193 362

a) We intend to test whether there is a difference in the proportion of men and women who smoke. Define the parameters, and state the Null and Alternative hypotheses

b) What proportion of men are smokers? What proportion of women are smokers? What is the difference between these proportions?

c) Using information associated with the plots on the next page o Which plot would you use to perform the test in part a)? o Let = 0.05, State your conclusion about whether there is a difference in the proportion of men and women who smoke - with a numerical reference from the appropriate plot

The fuel efficiency, measured in miles per gallon, was measured for each of 12 cars when the cars where brand new. After exactly 5 years of use, the fuel efficiency of the same 12 cars was measured again. The data is in the following table. Mileage when New Mileage after 5 years Difference 16 15 1 27 24 3 17 17 0 33 29 4 28 25 3 24 22 2 18 16 2 22 20 2 20 21 -1 22 20 2 29 22 7 21 22 -1 a). Construct a 99% CI for the mean difference between initial fuel efficiency and the fuel efficiency after 5 years. b). Do the data give an evidence that there is no difference in fuel efficiency.

The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's GPA.

Copy Data

part 1:  

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Part 2: find if a statistically significant relationship exists between the independent and dependent variables at .01 level of significance. Round to 3 decimal plaes. (ie. y= _+_x1+_x2, or not enough evidence)

The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 9 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.9. A random sample of 9 observations from another population revealed a sample mean of 27 and a sample standard deviation of 4.1. At the 0.01 significance level, is there a difference between the population means? State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject HO if T< or t> . b) Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) Pooled estimate of the population variance=? Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Test Statistic=?

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 13 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. 19 19 14 13 26 19 5 14 17 27 13 20 28 a. To compute the confidence interval use a distribution. b. With 90% confidence the population mean number of visits per physical therapy patient is between and visits. c. If many groups of 13 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per patient and about percent will not contain the true population mean number of visits per patient

The data are the ages of criminals and their victims.

1. Is there a significant correlation between the ages of the victims and the criminals? Provide support for your answer, and indicate the strength and direction of the correlation.
2. Conducting a simple linear regression, do they data support that a prediction of victim age can be obtained given the data provided in the file? Cite the elements of the output you used to draw your conclusion.
3. What is the equation of the regression, and what does that tell us?
4. How do correlation and regression differ?