You are testing the null hypothesis that there is no linear relationship between two​ variables, X and Y. From your sample of n=18, you determine that b1=4.4 and Sb1=1.3

a. What is the value of t stat?

b. At the a=0.05 level of​ significance, what are the critical​ values?

c. Based on your answers to​ (a) and​ (b), what statistical decision should you​ make?

d. Construct a​ 95% confidence interval estimate of the population​ slope,β1.

Suppose that we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birthweights are different than "normal". To test this hypothesis, a list of birthweights from 69 consecutive, full-term, live-born deliveries from the maternity ward of a hospital in a low-SES area is obtained. The mean birghweight is found to be 116 oz. Suppose that we know from nationwide surveys based on millions of deliveries that the mean birthweight in the United States is 120 oz, with a standard deviation of 23 oz. At α = .06, can it be concluded that the average birthweight from this hospital is different from the national average? (a) Find the value of the test statistic for the above hypothesis. (b) Find the critical value. (c) Find the p-value.

For high risk group screening (i.e. injection drug users) as compared to generla population screening, what is the best in terms of levels of sensitivity and specificity. Explain why.

3300 Econometric HW

Problem 2.

Use the data in the “Autocorrelation” tab to test

1. For Autocorrelation using the Durbin Watson Test

2. Graph the Residuals and determine whether they are distributed normally or whether they are biased

A biologist is sampling oranges to determine the amount of juice in each orange. She tested 50 oranges chosen at random. The average amount of juice was = 3.1 ounces with a standard deviation of σ = 0.4 ounces. Find a 95% confidence interval for the population mean number of ounces of juice in an orange.

elect one: a. 2.85 < μ < 3.35

b. 3.04 < μ < 3.16

c. 2.99 < μ < 3.21

d. 3.14 < μ < 3.21

Calculate ??/2 for each of the following. Illustrate your answers with graphs.

a. ? = 0.10

b. ? = 0.01

c. ? = 0.05

d. ? = 0.20

is there any scenarios when can a low R2 value be acceptable?

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

today (population 1) Five years ago (population 2)

sample mean 86 88

sample variance 112.5 54

sample size 45 36

The 92.50% confidence interval for the difference between the two population means is (round your answer to 2 decimal places).

In a multiple linear regression model with 2 predictors (X₁and X₂),                                TRUE     or     FALSE

In a multiple linear regression model with 2 predictors (X₁and X₂), then SSR(X₁)+SSR(X₂|X₁) = SSTO–SSE(X₁,X₂)   TRUE     or    FALSE

In a multiple linear regression model with 2 predictors (X₁and X₂), if X₁and X₂are uncorrelated, SSR(X₁) = SSR(X₁|X₂).       TRUE     or    FALSE

In a multiple linear regression model with 2 predictors (X₁and X₂), SSR(X₁) + SSR(X₂|X₁) = SSR(X₂) + SSR(X₁|X₂).       TRUE     or    FALSE

In simple linear regression, then (X’X)^-1is  2x2.    TRUE    or     FALSE

In simple linear regression, the hat-matrix is 2x2.    TRUE    or     FALSE

What other descriptive data would be useful for providing clues as to the causes of female breast cancer?

Television advertisers base their investment decisions regarding the promotion of their products and services on demographic information about television viewers. The age of the viewers is a key factor in their process. The following table shows the number of hours that a random sample of individuals watched television during the week. The individuals are grouped according to their ages. Minitab is required. You will need to enter the data into Minitab.

a. At the 0.05 level of significance, determine if there is a difference in the mean number of hours of television watched by age group. State your hypotheses and show all 7 steps clearly. (14 points)

b. Give and interpret the p-value. (3 points)

c. Should Tukey pairwise comparisons be conducted? Why or why not? (3 points)

d. If appropriate, use Minitab to produce Tukey pairwise comparison. Write a few sentences with your conclusions from those comparisons. (4 points)

e. Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision, and conclusion. Use the 0.05 level of significance. (8 points)

f. Verify with Minitab by attaching or including relevant output. (6 points)

A distribution and the observed frequencies of the values of a variable from a simple random sample of the population are provided below. Use the​ chi-square goodness-of-fit test to​ decide, at the specified significance​ level, whether the distribution of the variable differs from the given distribution. ​

Distribution: 0.3​, 0.2​, 0.2​, 0.2​, 0.1  

Observed​ frequencies: 12​, 9​, 8​, 17​, 4

Significance level = 0.10

Several years​ ago, a study of college freshmen found that 29.2​% of incoming freshmen characterized their political views as​ liberal, 46.6​% as​ moderate, and 24.2​% as conservative. For this​ year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views. Complete parts​ (a) and​ (b) below.

Liberal   145
Moderate   235
Conservative   120

Medical researchers have noted that adolescent females are much more likely to deliver low-birth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother's age. One such study is described in the article "Body Size and Intelligence in 6-Year-Olds: Are Offspring of Teenage Mothers at Risk?"† The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article and also with data published by the National Center for Health Statistics.

(c)

Find the equation of the least-squares regression line.

ŷ = ________ + (________) x

(g)

Use the regression line to predict for birth weight, in grams, of a baby born to a 15-year-old mother?

_________ g