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Statistics hmwrk

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Must show formulas used, and must explain how got to answer. Show work!

 

 

 

QUESTION 1

(a). (i)What is the distribution used for performing statistical inferences for one population standard deviation. (2 points)

(ii).What are the basic properties of the chi-square curves (4 points)

(b).For a  χ2-curve with 19 degrees of freedom, find the following by illustrating your work graphically.

(i). χ2-value that has an area 0.025 to its right (2 points)

(ii). χ2-value that has an area 0.05 to its right (2 points)

(iii). χ2-value that has an area 0.005 to its right (2 points)

(iv). χ2-value that has an area 0.95 to its right (2 points)

(c). For a  χ2-curve with df=8 of freedom, find the following by illustrating your work graphically

(i). χ2-value that has an area 0.01 to its left (2 points)

(ii). χ2-value that has an area 0.95 to its left (2 points)

(iii). χ2-value that has an area 0.025 to its left (2 points)

(iv). χ2-value that has an area 0.975 to its left (2 points)

 

 

 

 

 

QUESTION 2.

Gas mileage estimates for cars and light-duty trucks are determined and published by the Environmental protection Agency(EPA). According to the EPA,   “…the mileages obtained by most drivers will be within plus or minus 15% of the [EPA] estimates….”The mileage estimates given for one 2000 model is 23mpg on the highway. If the EPA claim is true, the standard deviation of mileages should be about 0.15×23/3=1.15mpg. A random sample of 12 cars of this model yields the following highway mileages.

24.1  23.3  22.5  23.2  22.3  21.1

21.4  23.4  23.5  22.8  24.5  24.3 

By using the critical value approach, at the 5% significance level, do the data suggest that the standard deviation of highway mileages for all 2000 cars of this model is different from 1.15mpg?  (20 points)

 

 

QUESTION 3

.(a) Define the following terminologies

 (i). Population Proportion (2 points)

(ii).Sample Proportion (2 points)

(b)(i).By using the sampling distribution of the sample proportion to make inferences about a population proportion, for samples of size n, what are the three conditions that need to be satisfied. (6 points)

(ii).State the assumptions of the one-proportion z-interval procedure (4 points)

(c). A  Reader’s Digest/Gallup Survey on the drinking habits of Americans estimated the percentage of adults across the country who drink beer, wine, or hard liquor, at least occasionally. Of the 1516 adults interviewed, 985 said that they drank.

(i). Determine a 95% confidence interval for the proportion, p, of all Americans who drink beer, wine, or hard liquor, at least occasionally. (2 points)

(ii). Determine a 90% confidence interval for the proportion, p, of all Americans who drink beer, wine, or hard liquor, at least occasionally. (2 points)

(iii).Interpret your results from part (i) and part (ii) .What can you conclude from the interpretation of these results. (3 points)

(iv). Determine a 95% confidence interval for the proportion, p, of all Americans who don’t drink beer, wine, or hard liquor, at least occasionally. (2 points)

(v). Determine a 90% confidence interval for the proportion, p, of all Americans who don’t drink beer, wine, or hard liquor, at least occasionally. (2 points)

(vi). Interpret your results from part (iv) and part(v) .What can you conclude from the interpretation of these results. (3 points)

 

 

 

QUESTION 4.

Body mass index (BMI) is a measure of the body fat based on height and weight. According to the document Dietary Guidelines for Americans, published by the U.S Department of Agriculture and the U.S Department of Health and Human Services, for adults, a BMI of greater than 25 indicates an above healthy weight(i.e., over-weight or obese). Of 750 randomly selected adults whose highest degree is bachelors, 386 have an above healthy weight; and of 500 randomly selected adults with a graduate degree, 237 have an above healthy weight.

(a). What are the assumptions required for using the two-proportion z-test here? (6 points)

(b). Apply the two-proportions z-test to determine, at the 5% significance level, whether the percentage of adults who have an above healthy weight is greater for those whose highest degree is a bachelors than for those with a graduate degree. (10 points)

(c). Repeat part (b) at the 10% significance level. (10 points)


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