Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Stat 1450 Final Exam Review

Example 1

The scatterplot below displays the price in dollars and quality rating for 14 different sewing machines.

(a) Describe the nature of the association between price and quality rating for the sewing machines.

(b) One of the 14 sewing machines substantially affects the appropriateness of using a linear regression model to predict quality rating based on price. Report the approximate price and quality rating of that machine and explain your choice.

Example 2

A survey organization conducted telephone interviews in December 2008 in which 1,009 randomly selected adults in the United States responded to the following question.

At the present time, do you think television commercials are an effective way to promote a new product?

Of the 1,009 adults surveyed, 676 responded “yes.” In December 2007, 622 of 1,020 randomly selected adults in the United States had responded “yes” to the same question. Do the data provide convincing evidence that the proportion of adults in the United States who would respond “yes” to the question changed from December 2007 to December 2008 ?

Example 3

A recent report stated that less than 35 percent of the adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city’s Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true.

The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a = 0.05 for the following hypotheses.

H0: p = 0.35 Ha: p < 0.35,

where p is the proportion of adult residents in the city who are able to pass the physical fitness test.

(a) Describe what a Type II error would be in the context of the study, and also describe a consequence of making this type of error.

(b) The Recreation Department recruits 185 adult residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, resulting in a p-value of 0.97 for the hypotheses stated above. If it was reasonable to conduct a test of significance for the hypotheses stated above using the data collected from the 185 volunteers, what would the p-value of 0.97 lead you to conclude?

(c) Describe the primary flaw in the study described in part (b), and explain why it is a concern.

Example 4

^{The Behavioral Risk Factor Surveillance System is an ongoing health survey system that tracks health conditions and risk behaviors in the United States. In one of their studies, a random sample of 8,866 adults answered the question “Do you consume five or more servings of fruits and vegetables per day?” The data are summarized by response and by age-group in the frequency table below.}

What is the probability that an adult who is ages 35-54 eats at least 5 servings of fruits or vegetables?

What is the conditional distribution of fruit and vegetable servings given that an adult is 55 or older?

Are Age-Group and Fruit/Vegetable Consumption independent? Show with a probability calculation.

Compute the expected count and Chi^2 contribution for the both cells in the 18-34 category.

^{Do the data provide convincing statistical evidence that there is an association between age-group and whether or not a person consumes five or more servings of fruits and vegetables per day for adults in the United States?}

Example 5

High cholesterol levels in people can be reduced by exercise, diet, and medication. Twenty middle-aged males with cholesterol readings between 220 and 240 milligrams per deciliter (mg/dL) of blood were randomly selected from the population of such male patients at a large local hospital. Ten of the 20 males were randomly assigned to group A, advised on appropriate exercise and diet, and also received a placebo. The other 10 males were assigned to group B, received the same advice on appropriate exercise and diet, but received a drug intended to reduce cholesterol instead of a placebo. After three months, post-treatment cholesterol readings were taken for all 20 males and compared to pretreatment cholesterol readings. The tables below give the reduction in cholesterol level (pretreatment reading minus post-treatment reading) for each male in the study.

Do the data provide convincing evidence, at the α = 0.01 level, that the cholesterol drug is effective in producing a reduction in mean cholesterol level beyond that produced by exercise and diet? 

Example 6

Windmills generate electricity by transferring energy from wind to a turbine. A study was conducted to examine the relationship between wind velocity in miles per hour (mph) and electricity production in amperes for one particular windmill. For the windmill, measurements were taken on twenty-five randomly selected days, and the computer output for the regression analysis for predicting electricity production based on wind velocity is given below. The regression model assumptions were checked and determined to be reasonable over the interval of wind speeds represented in the data, which were from 10 miles per hour to 40 miles per hour.

(a) Use the computer output above to determine the equation of the least squares regression line. Identify all variables used in the equation.

(b) Interpret the slope and intercepts. Does the intercept make sense?

(c) How much electricity would the windmill be expected to produce on a day when the wind velocity is 25 mph?

(d)  How much more electricity would the windmill be expected to produce on a day when the wind velocity is 25 mph than on a day when the wind velocity is 15 mph? Show how you arrived at your answer.

(e)  What proportion of the variation in electricity production is explained by its linear relationship with wind velocity?

Example 7

Every year, each student in a nationally representative sample is given tests in various subjects. Recently, a random sample of 9,600 twelfth-grade students from the United States were administered a multiple-choice United States history exam. One of the multiple-choice questions is below. (The correct answer is C.)

In 1935 and 1936 the Supreme Court declared that important parts of the New Deal were unconstitutional. President Roosevelt responded by threatening to

(A)  impeach several Supreme Court justices

(B)  eliminate the Supreme Court

(C)  appoint additional Supreme Court justices who shared his views

(D)  override the Supreme Court's decisions by gaining three-fourths majorities in both houses of Congress

Of the 9,600 students, 28 percent answered the multiple-choice question correctly.

Let p be the proportion of all United States twelfth-grade students who would answer the question correctly. Construct and interpret a 99 percent confidence interval for p.

Example 8

An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets.

(a)  What is the probability that Sam’s first upgrade will occur after the third flight?

(b)  Sam will take 104 flights next year. Would you be surprised if Sam receives more than 20 upgrades to first class during the year? Justify your answer.