Exam 22: Paired Samples and Blocks

A researcher wants to investigate whether people can concentrate as effectively in the morning if they do not eat breakfast.He will score some volunteers on reading comprehension tests.Some of the testing will be done after volunteers have eaten breakfast,and some testing will be done after volunteers have skipped breakfast.Design an experiment that will require a two-sample t-test to analyze the results.Design an experiment that will require a matched pairs t-test to analyze the results.Which experiment would you consider to be the stronger design?

An agricultural company wants to know if a new insecticide would increase corn yields.They will use test plots to collect observations with and without the insecticide.If they want to estimate the mean increase with a margin of error of 1.2 bushels per acre,with 99% confidence,estimate the minimum number of test plots they need.A previous study showed that the standard deviation of the increases was about 2.9 bushels per acre.

A researcher wishes to compare how students at two different schools perform on a math test.He randomly selects 40 students from each school and obtains their test scores.

The prices of 100 common products was recorded from two major supermarkets (Market A and Market B).It was observed that out of the 100 products,51 products were more expensive at Market A,34 products were more expensive at Market B,and 15 products were the same price.Is the median difference in price between items at these supermarkets different from 0? Carry out a Sign Test.Use a significance level of 0.05.

A coach uses a new technique in training middle distance runners.The times for 9 different athletes to run 800 metres before and after this training are shown below. A B C D E F G H I Time before training (seconds) 115.2 120.9 108.0 112.4 107.5 119.1 121.3 110.8 122.3 Time after training (seconds) 116.0 119.1 105.1 111.9 109.1 115.2 118.5 110.7 120.9 Construct a 99% confidence interval for the mean difference of the "before" minus "after" times if $\overline { \mathrm { d } } ( \text { before } - \text { after } ) = 1.222 \text { and } \mathrm { s } _ { \mathrm { d } } = 1.826$ .

A manufacturer has designed athletic footwear which it hopes will improve the performance of athletes running the $\text { 100-metre }$ sprint.It wishes to perform a hypothesis test to compare the times of athletes at the 100 metres with these shoes and with their usual shoes.

A test of writing ability is given to a random sample of students before and after they completed a formal writing course.The results are given below.Construct a 99% confidence interval for the mean difference between the before and after scores if $\overline { \mathrm { d } }$ (before - after)= 2.0 and sd =2.6457 $\text { Before } 70\quad80\quad92\quad99\quad93\quad97\quad76\quad63\quad68\quad71\quad74$ After 69 79 90 96 91 95 75 64 62 64 76

The owner of a large apartment complex had an in-ground swimming pool installed in an effort to increase tenant satisfaction.Nine tenants were randomly selected to complete a questionnaire that assessed their level of satisfaction with the apartment complex.Their scores before and after the installation of the pool are shown.The owner wants to assess the effectiveness of the pool in increasing tenant satisfaction. Tenant Number Level of Satisfaction Level of Satisfaction Before Pool After Pool 1 2 3 2 1 4 3 3 5 4 4 3 5 2 4 6 5 5 7 2 4 8 3 3 9 3 4

A study was conducted to determine if people consume more calories when they eat dinner while watching television.A random sample of ten people was selected to eat dinner one night in the dining room and the next night while watching television in the family room.The caloric content of their dinners was measured,and a 98% confidence interval for the difference in the means with and without the television, $\mu \mathrm { TV } - \mu ,$ was determined to be (-80,220).

The table below shows the weights of 9 subjects,in kg,before and after they followed a particular diet for two months. Subject A B C D E F G H I Before 75.6 81.0 70.7 59.4 90.9 55.8 85.5 94.5 77.0 After 72.9 80.1 65.3 56.3 77.0 56.7 81.0 87.8 73.4 Construct a 95% confidence interval for the mean difference of the "before" minus "after" weights if $\overline { \mathrm { d } }$ (before - after)= 4.4333 and sd = 4.2146

An agricultural company wanted to know if a new insecticide increases corn yields.Eight test plots showed an average increase of 3.125 bushels per acre when the insecticide was used compared to the previous year.The standard deviation of the increases was 2.911 bushels per acre.The company wants to use a paired t-test to determine the mean increase in yield.

A consumer is interested in investigating the difference in price between regular and premium gasoline at major filling stations in the U.S.A.An independent,random sample of stations is chosen and the prices per gallon are recorded for regular and premium gasoline.A histogram or Normal probability plot of the differences would be needed to verify the Nearly Normal Condition. Station Regular (\ /gal) Premium (\ /gal) A 1.62 1.75 B 1.52 1.59 C 1.32 2.12 D 2.02 2.14 E 1.98 2.21 F 1.83 1.89 G 1.65 1.91 1.91 2.02 I 1.75 1.89

A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys.She randomly selects 10 girls from the class and then randomly selects 10 boys.She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10.She does the same thing for the boys.

A high school coach uses a new technique in training middle distance runners.He records the times for 4 different athletes to run 800 metres before and after this training.A 98% confidence interval for the difference of the means before and after the training,μB - μA,was determined to be $( 2.5,4.7 )$

A coach uses a new technique in training middle distance runners.The times for 8 different athletes to run 800 metres before and after this training are shown below. Athlete Time before training (seconds) 115.6 115.6 113.7 118.6 118 119.9 110.7 119.5 Time after training (seconds) 116.2 114.3 111.3 119.4 116.2 120 107.1 115.6 Do the data suggest that,on average,the training helps to improve the athletes' times for the 800 metres? Perform a paired $\text { t-test }$ at the 5% significance level.