# VCU STAT 210 - Test 6 Practice Test #3 (1) (4 pages)

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## Test 6 Practice Test #3 (1)

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- Pages:
- 4
- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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Test 6 Practice Test 3 1 What is the point estimate of the population mean A 0 2 B Z C X D t E s In the current chapter covering statistical inferences on means all of the procedures we have discussed sampling distributions confidence intervals and statistical tests have involved two assumptions What are those two assumptions In the fall of 2011 VCU launched Spit for Science the VCU Student Survey www spit4science vcu edu This project is following the 2011 VCU freshman class across its college years and will also enroll new VCU freshman classes over the next few years The goal of the project is to understand how genetic and environmental factors come together to influence a variety of health related outcomes in the VCU undergraduate population 3 Since Spit for Science data is only collected for students in the 2011 VCU freshman class most of them are similar in age Suppose that when the project began the ages in months of all students in the 2011 VCU freshman class are skewed slightly to the right with a mean of 219 months and a standard deviation of 8 months If a simple random sample of 44 students in the 2011 VCU freshman class is selected and the age in months of each at the beginning of the program determined describe completely the sampling distribution of in the 2011 VCU freshman class X the resulting mean age of this sample of 44 students 4 Data was collected on multiple days and of interest is to estimate the mean number of students from which data has been collected each day since the project began For this problem only assume that the standard deviation of the number of students from which data has been collected each day since the project began for all days is 14 7 students What is the minimum number of days that would need to be selected for data collection to allow the calculation of a 99 confidence interval with margin of error no greater than 5 5 students Please circle your final answer 5 A simple random sample of 50 days was selected and the number of students from which data was collected each day was recorded The mean number of students per day for this sample of 50 days was 21 4 students with a standard deviation of 5 2 students and the distribution is skewed to the right If appropriate use this information to calculate and interpret a 99 confidence interval for the mean number of students from which data has been collected each day since the project began 6 In question 5 a confidence interval was computed based on a sample of 50 days If the number of days in the sample were decreased to 30 what impact would this have on the margin of error and width of the confidence interval A The margin of error would increase and the width would decrease B The margin of error would decrease and the width would increase C Neither the margin of error nor the width would be affected D Both the margin of error and the width would increase E Both the margin of error and the width would decrease 7 Of interest is to determine the mean number of minutes that all students in the 2011 VCU freshman class have spent discussing the Spit for Science project and since data for all students in the 2011 VCU freshman class is not available this mean cannot be determined It is conjectured that the mean number of minutes that all students in the 2011 VCU freshman class have spent discussing the Spit for Science project is 180 minutes and researchers want to test this versus the alternative that the mean number of minutes is different from 180 minutes State the appropriate null and alternative hypotheses that should be tested 8 Consider the information and hypotheses specified in question 7 It is known that some students have spent much time discussing the Spit for Science project and hence the distribution of time spent discussing is heavily skewed to the right Also assume that the standard deviation of the time spent discussing the Spit for Science project by all students in the 2011 VCU freshman class is 87 minutes To test the hypotheses in question 7 data for 22 students from the 2011 VCU freshman class enrolled in a STAT 210 class was recorded The mean number of minutes the students in the sample spent discussing the Spit for Science project was 203 minutes If appropriate use this information to test the hypotheses stated in question 7 at the 05 level of significance 9 Consider the three statements below Draw a circle around any if any and all that are valid statistical hypotheses H0 19 2 HA 97 H A X 16 10 The Freshman fifteen refers to an amount somewhat arbitrarily set at fifteen pounds of weight often gained during a student s first year at college With the population being all students in the 2011 VCU freshman class of interest is to test to see if the mean weight gain for this population of students is 15 pounds versus a conjecture supported by research at Ohio State University that the mean weight gain for all students in the 2011 VCU freshman class is actually less than 15 pounds State the appropriate null and alternative hypotheses that should be tested 11 Consider the information and hypotheses specified in question 10 A simple random sample of 61 students in the 2011 VCU freshman class was selected and the weight gain from when they arrived on campus in August 2011 until March 31 2012 was recorded for each If a student has lost weight the weight gain was recorded as a negative number The mean weight gain for this sample of 61 students was 9 7 pounds with a standard deviation of 12 3 pounds If appropriate use this information to test the hypotheses stated in question 10 at the 10 level of significance Test 6 Practice Test 3 Solutions X 1 C The sample mean 2 The assumptions are 1 Simple random sample 2 Normal population or large enough sample for the Central Limit Theorem to apply 3 We have a simple random sample and the sample size is large enough to apply the Central Limit Theorem n 44 15 So X N X is the point estimate of the population mean 219 X 8 n 44 1 206 since the CLT applies the shape is normal Hence 219 1 206 Z 2 2 576 14 7 m 5 5 2 6 885 2 47 4 Round up to 48 days 4 n 5 We have a simple random sample and the sample size is large enough for the Central Limit Theorem to apply n 50 15 so the assumptions are satisfied The population standard deviation is unknown so we must use the tdistribution df n 1 50 1 49 df 49 is not in the table so we will use df 50 99 CI implies t 50 2 678 So X t 50 sn 21 4 2 678 5 250 21 4 2 678 …

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