PRACTICE PROBLEMS for MIDTERM 3 in 2006 22S 30 105 Statistical Methods and Computing Spring 2005 Instructor Cowles Midterm 3 Show your work on any problems that involve calculations There are 30 total points on this midterm Point values for each question are shown in parentheses I will grade on a curve and will give partial credit wherever possible iv the proportion of all U S adults who favor increasing the use of nuclear power as a major source of energy v the proportion of people surveyed who favor increasing the use of nuclear power as a major source of energy vi none of the above c 1 Use the data given to calculate the point estimate of the proportion of all U S adults who favor increasing the use of nuclear power as a major source of energy numeric answer Name Course no 30 or 105 1 3 According to http www city data com city Iowa City Iowa html 34 6 of Iowa City residents are of German ancestry This information was obtained from a census and can be considered to be a correct value for the population You wish to interview a simple random sample of 500 residents of Iowa City What is the probability that your sample will contain at least 35 people of German ancestry Use Normal probability calculations 2 A Gallup Poll on energy use asked 512 randomly selected adults in the U S whether they favored increasing the use of nuclear power as a major source of energy Gallup reported that 225 said Yes d 1 2 What is the conventional symbol for the number you calculated in the previous problem circle one i ii iii iv v vi x p p s e 2 Are the assumptions regarding population size and sample size met so that you could use the normal approximation to calculate a 95 confidence interval for the proportion of interest yes no Briefly state each assumption and verify whether it is met in this problem a 1 2 What is the population of interest circle one i ii iii iv all adults in the U S the 512 adults surveyed the 225 who said Yes the proportion of all U S adults who favor increasing the use of nuclear power as a major source of energy v the proportion of people surveyed who favor increasing the use of nuclear power as a major source of energy vi none of the above f 2 Regardless of how you answered the previous question use the data given to calculate the 95 confidence interval b 1 2 What is the parameter of interest circle one i all adults in the U S ii the 512 adults surveyed iii the 225 who said Yes 1 2 g 1 2 What quantity are we 95 confident is in the interval you calculated circle one i ii iii iv v vi x p p s 3 To see how much difference time of day made on the speed at which he could download files a college sophomore performed an experiment He placed a file on a remote server and then proceeded to download it at three different time periods of the day 16 times in the morning at 7 00 a m 16 times in the evening at 5 00 p m and 16 times in the late night at midnight To choose his days and times of measurement he randomly selected 48 different days over a 120 day period and for each selected day he randomly determined whether he would do the download in the morning evening or late night For each download he measured the time in seconds a 1 The variable of interest is circle one i ii iii iv v time of day download time in seconds the size of the file the number of times downloaded none of the above b 1 5 The null hypothesis for the student s experiment could be stated informally as Time of day has no effect on download time Write this null hypothesis as a statement about population parameters using conventional symbols c 1 The type of hypothesis test that is most likely to be applicable for this problem is circle one i ii iii iv one sample t test Chi square test ANOVA linear regression d 1 What are the degrees of freedom for the test statistic for using the dataset described and the test you chose in the previous question Give either one or two numbers depending on which test you chose 3 4 NOTE There will not be any regression questions on midterm 3 in 2006 A question of this type could appear on the Final Every spring Nenana Alaska hosts a contest in which participants try to guess the exact minute that a wooden stand placed on the frozen Tanana River will fall through the breaking ice The contest started in 1917 as entertainment for railroad engineers It has grown into an event in which hundreds of thousands of entrants enter their guesses on the Internet and compete for prizes of more than 300 000 Because so much money depends on the time of ice breakup it has been recorded to the nearest minutie with great accuracy ever since 1917 An article in Science Climate Change in Nontraditional Datasets Oct 2001 p 811 used the data to investigate global warming by asking the question whether ice breakup had tended to occur earlier over time The dataset available to us contains two variables year julian the number of days from midnight on Jan 1 until the time of ice breakup Refer to the SAS output provided to answer the following questions a 1 The null hypothesis is that there is no linear relationship between year and time of ice breakup Write this null hypothesis as a statement about a population parameter Use conventional symbols b 1 The alternative hypothesis is that time of ice breakup decreases linearly over time Write this alternative hypothesis as a statement about a population parameter Use conventional symbols c 1 Give a point estimate and a 95 confidence interval for the population slope numeric answers d 2 Does your answer to the preceding question provide evidence in favor of the alternative hypothesis yes no Explain briefly If you could not answer the previous question pretend that the point estimate is 0 11 and the confidence interval is 0 21 0 01 and answer this question accordingly 4 e 1 5 What is the p value for the one sided test of no linear relationship between year and time of breakup f 1 5 Use the estimated regression equation to predict the time of breakup for this year 2005 Show your calculation g 1 On the SAS output circle the numbers that provide the endpoints of the interval in which you are 95 confident that this year s breakup time will lie Be sure to put your name on the SAS output h 1 Does the residual plot show evidence of severe outliers nonlinearity or inequality of variance yes no i 1 What proportion of the variability in time of breakup is explained by year numeric answer …